WATFORD, Circuit Judge

Timothy Allen Scott (argued) and Nicolas O. Jimenez, Scott Trial Lawyers APC, San Diego, California, for Defendant-Appellant Eric Gonzalez.

Katherine Kimball Windsor (argued), Law Office of Katherine Kimball Windsor, Pasadena, California, for Defendant-Appellant Fernando Luviano.

Jonathan I. Edelstein (argued) and Alan Ellis, Law Office of Alan Ellis, New York, New York for Defendant-Appellant Sussie Ayala.

Bram M. Alden (argued), Assistant United States Attorney, Criminal Appeals Section; Lawrence S. Middleton, Assistant United States Attorney Chief, Criminal Division; United States Attorney’s Office, Los Angeles, California; for Plaintiff-Appellee.

Before: John M. Rogers, Jay S. Bybee, and Paul J. Watford, Circuit Judges.

WATFORD, Circuit Judge:A group of law enforcement officers brutally beat Gabriel Carrillo, a visitor to the Los Angeles County Men’s Central Jail, while he was handcuffed. The defendants are three of the officers who played a role in the beating: Eric Gonzalez, a sergeant with the Los Angeles County Sheriff’s Department, and two deputies under his supervision, Fernando Luviano and Sussie Ayala. Ayala instigated the beating, Luviano physically participated in it, and Gonzalez summoned additional officers to the scene and oversaw the cover-up afterwards. A jury found the defendants guilty of violating Carrillo’s civil rights and falsifying reports to conceal their wrongdoing. On appeal, the defendants challenge mainly the sufficiency of the evidence to support their convictions and the district court’s refusal to dismiss an allegedly biased juror shortly after trial began. We affirm across the board.

I

On the day of the beating, Carrillo and his girlfriend, Griselda Torres, were visiting Carrillo’s brother at the jail. Gonzalez and Ayala were standing in an employee break room when another deputy, Pantamitr Zunggeemoge, brought Torres into the room to determine whether she had smuggled a cell phone into the facility in violation of jail regulations. After a search confirmed that she had, Torres told the officers that her boyfriend also had a cell phone. Gonzalez ordered Zunggeemoge, who cooperated with the government and testified against the defendants, to get Carrillo from the visitors’ lobby and bring him to the break room.

Zunggeemoge located Carrillo, cuffed his hands behind his back, and brought him to the break room. Once inside, Zunggeemoge pushed Carrillo face-first against a refrigerator and proceeded to search him while Gonzalez, Ayala, and Torres looked on. When Carrillo questioned the purpose of the search, Zunggeemoge lifted Carrillo’s arms "all the way up so he could feel some pain." After Zunggeemoge finished the search, Carrillo said to Torres, "If I wasn’t in handcuffs, this would be a different situation." Ayala walked over to Carrillo and demanded, "What did you say, what did you say?" Carrillo told Ayala that he had not been speaking to her.

At that point, Ayala summoned additional officers over her radio. Luviano and at least two other deputies responded to the call and entered the break room. As they surrounded Carrillo, Ayala told them, "You want to know what this homeboy said? He said that if he wasn’t in handcuffs, he’d take flight on us," meaning Carrillo would fight the officers. One officer proposed removing Carrillo’s handcuffs to "see how tough he is," while another suggested that they remove Torres from the break room.

After Torres was escorted out, Luviano punched the still-handcuffed Carrillo in the right side of his face. Luviano and Zunggeemoge then knocked Carrillo to the ground. Unable to break his fall, Carrillo landed on his face and stomach. Luviano and Zunggeemoge began punching Carrillo in the head, back, ribs, and thighs as he lay on the floor. Blood from Carrillo’s facial wounds soon covered the floor.Sergeant Gonzalez, who had been watching these events unfold, summoned additional officers over his radio using the code "415," a call indicating that a deputy is involved in a fight with an inmate. Two more deputies arrived and joined in punching and kicking Carrillo. At one point Carrillo lost consciousness; he testified at trial that when he came to, his head was "bouncing off the floor from the punches." To add insult to injury, Luviano pepper-sprayed Carrillo in the face, aggravating his wounds and making it difficult for him to breathe.

In all, the beating lasted about 45 seconds. Throughout, Carrillo remained handcuffed and unable to pose any resistance. As a result of the beating, he suffered bone fractures, trauma to the head and face, a broken nose, and multiple lacerations. Carrillo’s face was so disfigured by the beating that Torres could not recognize him when she saw him a few days later.

After Carrillo was carried out of the break room to receive medical attention, the officers huddled up to concoct a story that would justify their use of force. Sergeant Gonzalez, as the ranking officer, led the effort. He directed Zunggeemoge to prepare the primary incident report and largely dictated its contents. The report truthfully stated that Carrillo had been detained for possessing a cell phone and had been knocked to the floor, punched in the face, and pepper-sprayed. But the report falsely stated that Carrillo had attacked the officers and attempted to escape from their custody. According to the report, only one of Carrillo’s hands had been handcuffed during the incident, and he had used the handcuff dangling from his hand as a weapon by wildly swinging it at the officers. The officers’ use of force, under this telling, had been necessary to subdue a combative and resistant suspect.

Each of the three defendants prepared their own use-of-force reports repeating the agreed-upon cover story and describing their involvement in the incident. Of particular note, Gonzalez’s report stated that he had summoned additional officers to the scene and directed them to use force against Carrillo. Ayala’s report stated that she had helped Luviano and Zunggeemoge knock Carrillo to the floor. None of the witnesses who testified at trial corroborated Gonzalez’s claim that he had directed officers to use force or Ayala’s claim that she had used force against Carrillo.

Gonzalez also directed Zunggeemoge to prepare a probable cause declaration for use in prosecuting Carrillo. The account in the declaration tracked the false narrative contained in the officers’ reports. Based on the declaration, the district attorney’s office charged Carrillo with assaulting and resisting an officer and attempting to escape from custody.

Prosecutors dropped the charges against Carrillo after incriminating text messages between Gonzalez and another deputy surfaced, triggering an investigation into the circumstances leading up to the beating. The other deputy, who had arrested Carrillo’s brother two days before the beating, sent Gonzalez a text message attaching the booking photo of Carrillo’s brother showing his face cut and bruised. Gonzalez responded by sending the deputy Carrillo’s booking photo, which showed even more extensive injuries to Carrillo’s face. Gonzalez joked, "Looks like we did a better job .... Where’s my beer big homie."

The federal government charged Gonzalez, Luviano, and Ayala with violating Carrillo’s civil rights and falsifying reports of the beating. Count One of the indictment charged Gonzalez and Ayala with conspiring to deprive Carrillo of his civil rights, in violation of 18 U.S.C. § 241. Count Two charged all three defendants with willfully depriving Carrillo of his right to be free from the use of excessive force, in violation of 18 U.S.C. § 242. And Count Three charged each defendant with falsifying reports to obstruct an investigation, in violation of 18 U.S.C. § 1519.

After a five-day trial, the jury found the defendants guilty on all counts. The district court denied the defendants’ post-trial motions for judgment of acquittal or, in the alternative, a new trial. The court sentenced Gonzalez to 96 months of imprisonment, Luviano to 84 months, and Ayala to 72 months.

On appeal, the defendants each filed separate briefs advancing an assortment of arguments. Gonzalez and Ayala challenge the sufficiency of the evidence to support their convictions under 18 U.S.C. § 241. Luviano and Ayala challenge the sufficiency of the evidence to support their convictions under § 1519. All three defendants contend that the district court should have dismissed an allegedly biased juror shortly after the trial commenced. Gonzalez and Ayala contest one aspect of the jury instructions on the § 242 charge. Gonzalez contends that the government committed misconduct during closing arguments by asking the jury to draw factual inferences that the prosecutor knew to be false. And finally, Ayala challenges the substantive reasonableness of her 72-month sentence.

II

We begin with Gonzalez’s and Ayala’s challenge to the sufficiency of the evidence supporting their convictions under 18 U.S.C. § 241. As relevant here, § 241 prohibits two or more persons from "conspir[ing] to injure, oppress, threaten, or intimidate any person ... in the free exercise or enjoyment of any right or privilege secured to him by the Constitution or laws of the United States." Count One charged Gonzalez and Ayala with a § 241 conspiracy that had two objects: (1) to deprive Carrillo of his Fourth Amendment right to be free from the use of excessive force; and (2) to deprive Carrillo of his due process right not to be prosecuted on the basis of falsified evidence. The jury returned a general verdict finding both defendants guilty of Count One as charged. Gonzalez and Ayala concede that there was sufficient evidence to support the second object. They contend that the verdict on Count One must nevertheless be reversed because there was insufficient evidence to support the first object and the jury’s general verdict makes it impossible to tell which of the two objects the jury agreed upon.

A

Before addressing the defendants’ sufficiency challenge, we begin by rejecting the flawed premise of their argument. Gonzalez and Ayala assume that whenever one object of a multiple-object conspiracy is not supported by sufficient evidence, a general verdict must be set aside. The Supreme Court foreclosed that very argument in Griffin v. United States , 502 U.S. 46, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991). There, the Court held that reversal is required only if one of the objects of the conspiracy is legally deficient—for example, because the conduct underlying the object is protected by the Constitution, occurred outside the statute of limitations, or "fails to come within the statutory definition of the crime." Id. at 59, 112 S.Ct. 466. In that scenario, if the basis for the jury’s verdict is unclear, reversal is required because we do not expect jurors to be able to determine "whether a particular theory of conviction submitted to them is contrary to law." Id. ; see also Yates v. United States , 354 U.S. 298, 312, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957). The rule is different when all objects of the conspiracy are sound as a legal matter, but one of them lacks adequate evidentiary support. Because "jurors are well equipped to analyze the evidence," we can be confident that the jury chose to rest its verdict on the object that was supported by sufficient evidence, rather than the object that was not. Griffin , 502 U.S. at 59, 112 S.Ct. 466. In this latter scenario, the verdict stands.

This case is controlled by Griffin . Gonzalez and Ayala do not contend that either object of the conspiracy charged in Count One was legally deficient. They do not, for example, assert that the jury instructions improperly defined the elements of the crime. They argue only that the first object, concerning Carrillo’s right to be free from the use of excessive force, was not supported by sufficient proof. Even if we agreed with them on that point (which we don’t, for reasons explained below), they would not be entitled to reversal of their convictions on Count One. The evidence was sufficient to prove the second object, as they freely concede. That suffices to sustain the jury’s general verdict against the challenge Gonzalez and Ayala assert. See id.

Although the Supreme Court’s 1991 decision in Griffin provides the rule that controls here, Gonzalez and Ayala contend that our court established a contrary rule in United States v. Manarite , 44 F.3d 1407 (9th Cir. 1995). In that case, they say, we reversed a general verdict convicting the defendants of a multiple-object conspiracy where two of the five objects (mail and wire fraud) were not supported by sufficient evidence. Gonzalez and Ayala are wrong. In Manarite , we held that the fraudulent scheme underlying the mail and wire fraud objects "did not constitute mail or wire fraud as a matter of law." Id. at 1413. To put it in the language of Griffin , the conduct charged by the government, even if proved by sufficient evidence, did not "come within the statutory definition of the crime." 502 U.S. at 59, 112 S.Ct. 466. Because the jury could not have been expected to recognize that legal deficiency, we reversed the defendants’ convictions. We did not hold—and indeed, in light of Griffin , could not have held—that the defendants were entitled to reversal of their convictions because the evidence was insufficient to prove the charged conduct itself.

In short, we affirm Gonzalez’s and Ayala’s conspiracy convictions under § 241 regardless of whether there was sufficient evidence to support the first object of the charged conspiracy, since it is undisputed that sufficient evidence exists to support the second object.

B

We must nonetheless resolve Gonzalez’s and Ayala’s sufficiency challenge because their convictions for the substantive offense charged in Count Two are predicated on Pinkerton v. United States , 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946). Under Pinkerton , a defendant may be found guilty of a criminal offense committed by his co-conspirators if (1) the offense was committed during the course and in furtherance of the conspiracy, (2) the defendant was a member of the conspiracy at the time the offense was committed, and (3) the offense fell within the scope of the unlawful agreement and could be "reasonably foreseen as a necessary or natural consequence of the unlawful agreement." Id. at 647–48, 66 S.Ct. 1180 ; see United States v. Gadson , 763 F.3d 1189, 1215 (9th Cir. 2014). Here, the government argued at trial that if Gonzalez and Ayala conspired to deprive Carrillo of his right to be free from the use of excessive force, as charged in the first object of Count One, they were also guilty under Pinkerton of the substantive offense committed by their co-conspirators as charged in Count Two. Gonzalez and Ayala do not contest these general principles. They contend that Pinkerton liability cannot apply because the government failed to prove that they in fact conspired to commit the first object of the conspiracy as charged in Count One.

The same general rules governing proof of conspiracies elsewhere in the criminal law apply under § 241, although no overt act is required. United States v. Skillman , 922 F.2d 1370, 1375–76 (9th Cir. 1990). In order to convict Gonzalez and Ayala of violating § 241 based on the first object of the charged conspiracy, the government had to prove: (1) that two or more persons agreed to deprive Carrillo of his right to be free from the use of excessive force, and (2) that Gonzalez and Ayala knowingly joined the agreement and intended to deprive Carrillo of his right to be free from the use of excessive force. See id. at 1373. In evaluating a sufficiency-of-the-evidence challenge, we ask whether, viewing the evidence in the light most favorable to the government, any rational jury could have found each element of the offense beyond a reasonable doubt. Jackson v. Virginia , 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979).

The first element requires proof of an agreement among the conspirators to commit a crime—here, a violation of 18 U.S.C. § 242. The government does not need to prove the existence of an express agreement; a tacit agreement will suffice. United States v. Reese , 2 F.3d 870, 893 (9th Cir. 1993). A tacit agreement may be inferred from the conspirators’ conduct as well as other circumstantial evidence. United States v. Duenas , 691 F.3d 1070, 1085 (9th Cir. 2012).

None of the officers involved in the beating ever said to each other, "Let’s get together and use excessive force against Carrillo." But there was more than sufficient evidence of a tacit agreement to do just that. Ayala instigated the beating by summoning other officers to the break room, despite the fact that Carrillo was handcuffed, under control, and not being combative. When Luviano and the other officers arrived, Ayala made clear that she had summoned them not to help quell a fight, but to start one. She informed the assembled officers, in a manner that the jury could conclude was intended to goad her colleagues into taking retaliatory action, that Carrillo had said he would fight the officers if he weren’t in handcuffs. One of the officers suggested that they remove Carrillo’s girlfriend from the break room, thereby eliminating the only non-officer witness to what was about to happen. Everyone present understood at that point that Carrillo would be taught a lesson for making his remark. After acting together to punish Carrillo for his perceived insolence, the officers then engaged in a concerted effort to cover up their wrongdoing.

A rational jury could infer from this evidence that the officers tacitly agreed to use excessive force against Carrillo. The officers shared a common motive—to punish Carrillo. They acted together to achieve that objective by repeatedly punching and kicking him. And they huddled together afterward to come up with an agreed-upon story that would justify their actions, a story each of the officers repeated in the falsified reports they submitted. Taken together, these facts—a common motive, joint action in pursuit of a common objective, and a coordinated cover-up—suffice to support the existence of a conspiracy. See, e.g. , United States v. Navarrette-Aguilar , 813 F.3d 785, 794 (9th Cir. 2015) ; United States v. Smith , 294 F.3d 473, 478–79 (3d Cir. 2002) ; United States v. Davis , 810 F.2d 474, 477 (5th Cir. 1987). With respect to the second element, a rational jury could also have found that Gonzalez and Ayala knowingly joined the conspiracy and intended to deprive Carrillo of his right to be free from the use of excessive force. As to Gonzalez, the jury could rely on the fact that, after witnessing the events that led to Carrillo’s beating, Gonzalez summoned additional officers to the break room even though he knew there was no legitimate law enforcement purpose for doing so. Carrillo was already on the ground in handcuffs being pummeled by multiple officers. Viewed in the light most favorable to the government, Gonzalez’s summoning of additional officers proved that he shared the other officers’ desire to see Carrillo punished and that he wanted to make sure the objective was achieved. In addition, Gonzalez stated in his report that he directed the officers under his command to use force against Carrillo. Gonzalez contends that the government cannot rely on this statement because the indictment charged Gonzalez in Count Three with having falsified his report. But the jury could reasonably conclude that some of the statements in Gonzalez’s report were accurate, even if the report falsely recited other facts in an attempt to justify the officers’ actions. Finally, Gonzalez’s participation in a coordinated cover-up with the officers who inflicted the beating strengthened the inference that he was in on the agreement to use excessive force against Carrillo, rather than merely present at the scene of a crime committed by others.

The evidence also supports the jury’s finding that Ayala knowingly joined the conspiracy and shared the intent to see Carrillo punished through the use of excessive force. As noted above, a rational jury could conclude that she instigated the beating by summoning additional officers to the break room for no legitimate reason, and by goading her fellow officers into assaulting Carrillo without justification. That was enough to make her a member of the conspiracy; she need not have intended to participate in the unlawful assault herself. See Ocasio v. United States , ––– U.S. ––––, 136 S.Ct. 1423, 1429, 194 L.Ed.2d 520 (2016) ; United States v. Whitney , 229 F.3d 1296, 1301–02 (10th Cir. 2000). As with Gonzalez, Ayala’s participation in the coordinated cover-up further supports the inference that she acted in concert with the other officers to use excessive force against Carrillo and was not merely an uninvolved bystander who happened to witness his beating.

III

We turn next to Luviano’s and Ayala’s argument that the evidence is insufficient to sustain their convictions under 18 U.S.C. § 1519. That statute provides:

Whoever knowingly alters, destroys, mutilates, conceals, covers up, falsifies, or makes a false entry in any record, document, or tangible object with the intent to impede, obstruct, or influence the investigation or proper administration of any matter within the jurisdiction of any department or agency of the United States or any case filed under title 11, or in relation to or contemplation of any such matter or case, shall be fined under this title, imprisoned not more than 20 years, or both.

The district court properly instructed the jury that the government bore the burden of proving that: (1) the defendants knowingly falsified a record or document; (2) the defendants acted with the intent to impede, obstruct, or influence an actual or contemplated investigation; and (3) the investigation concerned a matter within the jurisdiction of the U.S. Department of Justice or the Federal Bureau of Investigation. See United States v. Katakis , 800 F.3d 1017, 1023 (9th Cir. 2015). The court also properly instructed the jury that the government did not need to prove that the defendants knew about a pending federal investigation or that they intended to obstruct a specific federal investigation. Luviano and Ayala do not contest these instructions. They contend only that the evidence was insufficient to satisfy the elements as defined.

Viewed in the light most favorable to the government, the evidence introduced at trial amply supported the defendants’ convictions. Luviano and Ayala filed their own narrative reports that provided a false account of the events leading up to Carrillo’s beating, and the evidence leaves no doubt that the defendants knew their reports were false when they prepared them. The evidence also established that the defendants prepared their reports with the intent to obstruct a contemplated investigation into whether the force used against Carrillo was reasonable. The whole point of the officers’ efforts to concoct a false cover story was to make it appear as though the force they used was justified, thereby shielding them from the punishment that would likely follow if the truth were revealed. And as to the third element, the defendants stipulated that the "matter" at issue here—an inquiry into whether the officers’ actions violated Carrillo’s civil rights—falls within the jurisdiction of both the U.S. Department of Justice and the FBI.

In the face of this plainly sufficient evidence, Luviano and Ayala assert three legal arguments concerning the scope of § 1519.

First, they argue that § 1519 applies only to financial records or documents, not to reports prepared by law enforcement officers. They base that argument largely on the fact that Congress enacted § 1519 as part of the Sarbanes-Oxley Act of 2002, which was "intended to prohibit, in particular, corporate document-shredding to hide evidence of financial wrongdoing." Yates v. United States , ––– U.S. ––––, 135 S.Ct. 1074, 1081, 191 L.Ed.2d 64 (2015) (plurality opinion). But the text of § 1519 covers "any record, document, or tangible object," and the statute’s intent clause encompasses the intent to impede, obstruct, or influence the investigation of "any matter within the jurisdiction of any department or agency of the United States." If Congress had intended to limit the statute’s scope to records or documents of a financial nature, it could not have chosen language more ill-suited to convey that narrow focus. Nor is there anything in the legislative history of § 1519 that supports the defendants’ restrictive reading of the statute. Indeed, the relevant Senate report indicates that the drafters intended the statute to have a decidedly more expansive reach. See S. Rep. No. 107-146, at 14 (2002) (" Section 1519 is meant to apply broadly to any acts to destroy or fabricate physical evidence so long as they are done with the intent to obstruct, impede or influence the investigation or proper administration of any matter, and such matter is within the jurisdiction of an agency of the United States ...."). We therefore hold what several other circuits have assumed to be true: Reports prepared by law enforcement officers qualify as "records" or "documents" under § 1519. See United States v. McQueen , 727 F.3d 1144, 1151–53 (11th Cir. 2013) (upholding § 1519 conviction predicated on falsified police report); United States v. Moore , 708 F.3d 639, 649 (5th Cir. 2013) (same); United States v. Moyer , 674 F.3d 192, 206–08 (3d Cir. 2012) (same); United States v. Gray , 642 F.3d 371, 374–79 (2d Cir. 2011) (same).

Second, Luviano and Ayala argue that the government failed to prove that they "falsified" their reports. In their view, that term covers only the alteration of existing records or documents, not the wholesale fabrication of new ones. That would be an odd distinction for Congress to draw in a statute designed to punish efforts to obstruct investigations conducted by the federal government. After all, government investigations can be obstructed just as readily by creating false documents as by altering documents that already exist.

We agree with the Second Circuit that Congress did not draw the implausible distinction the defendants have proposed. As the court explained in United States v. Rowland , 826 F.3d 100 (2d Cir. 2016), the word "falsify" has two meanings relevant in this context: (1) to modify or tamper with an object, and (2) to make false representations. Id . at 108. The first definition supports the defendants’ argument, but the second one obviously does not. A defendant can make false representations both by modifying an existing document in a way that obscures the truth, and by creating a fabricated document from whole cloth. We think Congress used the term "falsifies" to encompass both of these acts, a reading that again is supported by the statute’s legislative history. See S. Rep. No. 107-146, at 12 (proposed statute "would clarify and plug holes in the current criminal laws relating to the destruction or fabrication of evidence") (emphasis added). We join the Second Circuit in holding that § 1519 prohibits the creation of false documents and the alteration of existing documents. Rowland , 826 F.3d at 108–09.

Finally, Luviano and Ayala argue that the government failed to prove that they acted with the requisite intent. They contend that they lied in their reports solely to support the prosecution of Carrillo on false charges, not to obstruct or impede an investigation into their own wrongdoing. Viewed in the light most favorable to the government, a rational jury could conclude that the evidence showed otherwise. Zunggeemoge testified that the officers falsified their reports to justify their use of force against Carrillo. He explained that the officers needed to lie about what happened because the force they used was excessive and they would get in trouble if the truth were known. This evidence supported the jury’s finding that the defendants contemplated an investigation into their use of excessive force and falsified their reports to obstruct or impede such an investigation.

In a supplemental letter submitted after the close of briefing, Luviano and Ayala cite United States v. Johnson , 874 F.3d 1078 (9th Cir. 2017), in support of their position. That case is of no help to them. Johnson involved a different obstruction-of-justice statute that requires proof of an intent to hinder, delay, or prevent the communication of information "to a law enforcement officer or judge of the United States." 18 U.S.C. § 1512(b)(3). In Johnson , we held that this statute requires the government to prove a "reasonable likelihood" that the information in question would have reached a federal officer. 874 F.3d at 1081 (citing Fowler v. United States , 563 U.S. 668, 677–78, 131 S.Ct. 2045, 179 L.Ed.2d 1099 (2011) ). Section 1519 does not contain an element requiring such proof. To sustain a conviction under § 1519, it is enough for the government to prove that the defendant intended to obstruct the investigation of any matter as long as that matter falls within the jurisdiction of a federal department or agency. Moyer , 674 F.3d at 209–10 ; United States v. Gray , 692 F.3d 514, 519 (6th Cir. 2012). The defendant need not know that the matter in question falls within the jurisdiction of a federal department or agency. McQueen , 727 F.3d at 1152 ; Moyer , 674 F.3d at 208. As discussed above, the government introduced more than enough evidence to prove that the defendants acted with the intent required under § 1519.

IV

All three defendants challenge the district court’s denial of their request to dismiss a juror for actual or implied bias shortly after the trial began. A district court’s actual bias determination is reviewed for abuse of discretion because assessing a juror’s impartiality often turns on an evaluation of the juror’s demeanor and credibility. United States v. Gonzalez , 214 F.3d 1109, 1112 (9th Cir. 2000). A district court’s implied bias determination involves a mixed question of law and fact that we review de novo . Fields v. Brown , 503 F.3d 755, 770 (9th Cir. 2007) (en banc).

The issue of alleged juror bias arose in the following circumstances. During opening statements, the government displayed a photograph of Carrillo’s face taken shortly after the beating. The photograph, which was later admitted into evidence, graphically depicted the injuries Carrillo sustained as a result of the beating. The next day, after the first few witnesses had been called, the district court received a note from one of the jurors. The juror stated that seeing the image of Carrillo’s disfigured face "sickened and saddened my core being"; the image, she said, "kept replaying in my head throughout the night." The juror explained that she understood all of the instructions the court had given; that she would "continue to listen to the facts as presented"; and that she understood the government bore the burden of proving the defendants’ guilt beyond a reasonable doubt. "However," the letter concluded, "the grotesque image of injuries sustained by Gabriel Carrillo is weighing heavy on my heart and I felt compelled to share my struggles with you."

After reviewing the letter with counsel, the district court conducted an extensive colloquy with the juror outside the presence of the other jurors. When first asked by the court whether she could consider all of the evidence and render a fair and impartial verdict, the juror responded, "Cognitively, yes. Emotionally, I’m not sure." When the court followed up and asked whether she would be able to keep her emotions in check and not allow them to override her ability to reason objectively and impartially, the juror said, "I would like to say yes, I could." But, she added, "I was not able to sleep last night. I did not eat dinner." Later in the colloquy, the juror said that she would "listen to all the evidence as it’s presented." In response to the court’s final question, which asked whether the juror believed she could continue to serve by not allowing any single item of evidence "to totally override your reasoning, your analysis, your impartiality," the juror answered without qualification, "Yes." On the basis of this last answer and an assessment of the juror’s demeanor, the district court concluded that the juror could be fair and impartial. The court accordingly denied the defendants’ request to dismiss her.

The defendants contend that the record establishes both actual and implied bias that compelled the juror’s dismissal. Actual bias exists when, as the term suggests, a juror is in fact biased for or against one of the parties, thereby precluding her from rendering a fair and impartial verdict. Fields , 503 F.3d at 767. Most of the cases in which actual bias has been found involved jurors who either stated that they could not be impartial or who, after expressing views adverse to one party, equivocated when asked if they could set aside those views and evaluate the evidence fairly and impartially. Id. Implied bias is different. It is a legal doctrine under which bias will be conclusively presumed in certain circumstances even if the juror professes a sincere belief that she can be impartial. Dyer v. Calderon , 151 F.3d 970, 981–82 (9th Cir. 1998) (en banc).

We can quickly dispose of the claim that the record warrants a finding of implied (presumed) bias. Implied bias arises only in a few "extreme situations." Fields , 503 F.3d at 770. We have held that bias will be presumed "where the relationship between a prospective juror and some aspect of the litigation is such that it is highly unlikely that the average person could remain impartial in his deliberations under the circumstances." Id. (internal quotation marks omitted). Examples of such relationships include having a relative who is a participant in the trial, or having had "some personal experience that is similar or identical to the fact pattern at issue in the trial." Gonzalez , 214 F.3d at 1112 ; see Dyer , 151 F.3d at 982 ; Tinsley v. Borg , 895 F.2d 520, 528 (9th Cir. 1990). Bias will also be presumed when "the juror is aware of highly prejudicial information about the defendant," which no ordinary person could be expected to put aside in reaching a verdict. Gonzalez , 214 F.3d at 1112. And we have held that bias will be presumed when a juror lies about material facts during voir dire in order to secure a spot on the jury. Dyer , 151 F.3d at 982.

None of these circumstances is present here. The juror in our case did not lie about material facts during voir dire , and she was not aware of any highly prejudicial information about the defendants. Nor did she have a relationship to some aspect of the case that would make it highly unlikely she could remain impartial. What caused her to raise concerns about her impartiality was her strong reaction to an item of evidence properly admitted at trial. Without more, that reaction cannot be the basis for an implied bias claim. One of the primary functions of the Federal Rules of Evidence, particularly Rules 403 and 404, is to prevent the admission of evidence that might render jurors unfairly biased against one of the parties. We do not presume that jurors become "biased" as a result of exposure to evidence properly put before them. Here, the photograph depicting Carrillo’s injuries was properly admitted as an exhibit at trial, so no presumption can arise that jurors exposed to it would be unable to decide the case fairly and impartially. The juror’s reaction to the photograph could at most support a claim of actual bias, to which we turn next.

We do not think the record supports a claim of actual bias either. To be sure, the juror in question raised concerns about her ability to remain impartial after seeing the photograph of Carrillo. But the district court conducted a thorough colloquy with the juror to determine whether she could still fairly and impartially evaluate all of the evidence presented. While the juror expressed initial reservations about her ability to do so on an emotional level, she maintained throughout that she could do so "cognitively." The only question was whether the juror could set aside her emotional reaction to the photograph and allow her cognitive assessment of the evidence to control. After a dialogue with the court, the juror unequivocally stated that she could evaluate all of the evidence impartially, notwithstanding her strong reaction to the photo. The district court had the opportunity to assess the juror’s demeanor and concluded that her assurance was credible. We see nothing in the record that would justify second-guessing the district court’s conclusion.

The facts of this case are similar to those in Bashor v. Risley , 730 F.2d 1228 (9th Cir. 1984), where we also rejected a claim of actual bias. There, during voir dire , defense counsel in a murder case asked a juror whether she thought she could be impartial, given that the victim’s daughter had been a student in the juror’s dance class. Id . at 1236 n.3. The juror candidly responded that she did not think she could be. Id . When questioned by the prosecutor, however, the same juror said that she could be impartial "on the facts." Id . at 1236 n.4. When the trial court inquired about this apparent inconsistency, the juror responded that the defense attorney had asked about her emotions, whereas the prosecutor had asked about her ability to evaluate the facts. Id . at 1237. The juror confirmed that she could put her emotions aside, and the trial court ultimately concluded that she could be impartial. After conducting an independent review of the record, we upheld the trial court’s ruling. We reasoned that the juror had recognized her responsibility to decide the case based on the evidence presented at trial, and we emphasized that when the juror was advised of her duties she assured the judge that "she could be a fair juror and decide the case on the proved facts." Id .

The same analysis governs here. Like the juror in Bashor , the juror in our case made statements, both in her note to the court and at the outset of the colloquy, that raised legitimate concerns about her ability to render a fair and impartial verdict. But after questioning the juror to explore those concerns, the district court received the juror’s unqualified assurance that she could decide the case impartially based on the evidence presented. As in past cases involving similar facts, the court did not abuse its discretion in concluding that no actual bias had been shown. See United States v. Alexander , 48 F.3d 1477, 1484 (9th Cir. 1995) ; United States v. Daly , 716 F.2d 1499, 1507 (9th Cir. 1983).

The defendants make one last argument, which is that the district court should have conducted further inquiry into the same juror’s alleged bias later in the trial. They assert that, during the government’s case-in-chief, the juror looked away when (1) the photograph depicting Carrillo’s injuries was again displayed, and (2) the government played a videotape of an interview that sheriff’s deputies conducted with Carrillo shortly after he was beaten. This behavior, the defendants contend, constituted further evidence of actual bias that the district court was obligated to investigate.

The district court did not abuse its discretion in concluding, without further investigation, that the juror’s conduct did not amount to evidence of actual bias. The court was not required to make any further inquiry into the juror’s reasons for looking away from the photograph because that same photo had been the basis of the earlier colloquy. Thus, the court already knew "the exact scope and nature of the bias allegation." United States v. Smith , 424 F.3d 992, 1011 (9th Cir. 2005) (internal quotation marks omitted). As to the suggestion that the juror may have looked away from the video of Carrillo’s interview, the court pointed out that the juror could still hear the audio of the interview. And if she did not want to look at Carrillo’s bloodied and battered image in the video, it was presumably for the same reasons she did not want to view the photograph again. In these circumstances, the district court had no obligation to engage the juror in a second round of questioning.

V

Gonzalez and Ayala argue that the district court gave the jury faulty instructions with respect to Count Two, which charged a violation of 18 U.S.C. § 242. (We need not decide whether Luviano preserved this argument on appeal since the argument fails in any event. Luviano did not raise this argument in his opening brief, and he did not join the arguments raised by his co-defendants until his reply brief.) The defendants do not challenge the instructions given on the offense’s core elements. Instead, they focus on a provision of § 242 that increases the maximum term of imprisonment "if bodily injury results from the acts committed in violation of this section." The district court instructed the jury on this element of the offense as follows: "If you find a defendant guilty as charged in Count Two of the indictment, you must then determine whether the government has proven beyond a reasonable doubt that Mr. Carrillo suffered a bodily injury, and that the bodily injury resulted from acts committed by that defendant."

The defendants argue that this instruction was deficient because it did not require the jury to find that each defendant’s acts were the "proximate cause" of Carrillo’s injuries. The defendants did not request an instruction on proximate cause, so we review only for plain error. United States v. Vincent , 758 F.2d 379, 383 (9th Cir. 1985).

The "bodily injury" element of § 242 is similar to a comparable provision found in 21 U.S.C. § 841, a statute criminalizing the distribution of certain controlled substances. Section 841 provides for enhanced penalties "if death or serious bodily injury results from the use of such substance." § 841(b)(1)(C). In United States v. Houston , 406 F.3d 1121 (9th Cir. 2005), we held that Congress’ use of the phrase "results from" indicates that proof of but-for causation alone is required. We explicitly rejected the defendant’s contention that proximate cause also had to be shown. Id. at 1124. Because § 242 employs the same "results from" phrase we construed in Houston , the district court’s failure to give a proximate cause instruction cannot be deemed an error so obvious that it should have been avoided even without an objection having been made.

The defendants argue that Burrage v. United States , 571 U.S. 204, 134 S.Ct. 881, 187 L.Ed.2d 715 (2014), requires a contrary result. In that case, the Supreme Court considered the same statutory provision at issue in Houston and held, as we did, that the statute’s plain language requires a showing of but-for causation. Id. at 214, 134 S.Ct. 881. The Court expressly declined to address whether proximate cause must also be shown. Id. at 210, 134 S.Ct. 881. As a result, nothing in Burrage calls into question the reasoning or result in Houston.

VI

Gonzalez asserts that the government committed misconduct during closing arguments by asking the jury to draw inferences from the evidence that the prosecutor knew to be false. Specifically, the government argued that Gonzalez could be found guilty of violating §§ 241 and 242 on the theory that he ordered his subordinates to use excessive force against Carrillo. As the basis for this argument, the government relied on Gonzalez’s use-of-force report, in which Gonzalez stated that he personally directed deputies to use force against Carrillo. On appeal, Gonzalez contends that the government’s argument was improper because the prosecutor knew that Gonzalez’s report was false. Gonzalez did not object to the statements he now challenges, so we review only for plain error. See United States v. Geston , 299 F.3d 1130, 1134 (9th Cir. 2002). There was no error, plain or otherwise.

Gonzalez is correct that a prosecutor may not ask the jury to draw inferences that the prosecutor "knows to be false, or has very strong reason to doubt." United States v. Blueford , 312 F.3d 962, 968 (9th Cir. 2002). But the prosecutor did not cross that line here. The prosecutor had a good-faith basis for arguing to the jury that Gonzalez directed others to use force because Gonzalez’s own use-of-force report said that is what he did. As Gonzalez points out, none of the witnesses who testified at trial corroborated that assertion, which certainly undercuts the strength of the inference that can be drawn from the statements in Gonzalez’s report. Still, notwithstanding the absence of witness corroboration, Gonzalez’s own lawyer argued that Gonzalez had in fact directed others to use force. Gonzalez’s lawyer argued that everything Gonzalez said in his report was true, presumably to help win his client’s acquittal on the offense charged in Count Three. The government was entitled to argue, and the jury was entitled to find, that some aspects of Gonzalez’s report were true while others were false, based on the totality of the evidence introduced at trial. The government did not commit misconduct by inviting the jury to credit as true something that Gonzalez’s own lawyer asserted was true.

VII

Finally, Ayala contends that her 72-month sentence is substantively unreasonable. There is no merit to this argument. The court granted Ayala a downward departure from the 87–108 months she faced under the Sentencing Guidelines. Although a below-Guidelines sentence is not immune from challenge, such a sentence will rarely be substantively unreasonable. See United States v. Armstrong , 620 F.3d 1172, 1179 (9th Cir. 2010).

The district court adequately explained why it believed the sentencing factors described in 18 U.S.C. § 3553(a) justified a departure down to 72 months but no lower. Most significantly, Ayala instigated the assault on Carrillo, first by summoning additional officers to the break room for no legitimate law enforcement purpose, and then by goading her colleagues into attacking Carrillo while he stood defenseless in handcuffs. Ayala not only failed to report the gross abuse of authority she and her colleagues had participated in; she affirmatively tried to cover up their wrongdoing by filing a false report, which she knew would be used to support Carrillo’s prosecution on felony charges that were completely fabricated. The district court properly concluded that Ayala’s actions exhibited "a profound disrespect for the law" and the people Ayala was sworn to serve. The court did not abuse its discretion when it sentenced her to 72 months in prison.

AFFIRMED.