Alexander Egbuniwe and Celestine Any-anwu appeal from the judgments entered upon their convictions for violations of federal narcotics laws. They assert that the district court abused its discretion in excusing a juror and allowing an eleven-person jury to return a verdict. In addition, Eg-buniwe asserts the district court erred in calculating his sentence based on the amount of heroin possessed by the other members of the conspiracy. We affirm because we conclude that the district court acted within its discretion in proceeding with eleven jurors pursuant to Rule 23(b) of the Federal Rules of Criminal Procedure. We also hold that the district court correctly calculated Egbuniwe’s sentence based on his involvement in the conspiracy.

Pertinent Factual Background

Onyedi Lawrence Irokameje, Richard 0. Arum, Okwudiri Remi Arishi, and Celestine Emere Anyanwu were arrested for narcotics offenses after arriving in Los Angeles International Airport on a flight from Lagos, Nigeria. Irokameje, Arum, and Any-anwu had transported heroin from Nigeria by carrying it in their digestive tracts. The record demonstrated that Alexander Eg-buniwe and Ijemba Alexander Ifeanyi (Ijemba) were involved in a conspiracy with Irokameje, Arum, Arishi, and Anyanwu to distribute heroin imported from Nigeria.

Egbuniwe, Arishi, and Anyanwu were tried jointly. The jury began deliberating on February 20, 1991 at 10:25 a.m. At 4:00 p.m., the jury sent the district court a note stating in part: “And we are very much a hung jury. Do you have any instruction for us?” The district court did not give the jury any further instructions.

The next day, while the jury was in deliberations, Juror Number 8's neighbor requested permission to speak with Juror Number 8 as soon as possible. The neighbor told the court that Juror Number 8’s wife had been arrested. In an informal discussion before the court proceedings began, the neighbor told counsel that Juror Number 8’s wife had been arrested for nonpayment of traffic tickets. The attor neys informed the court of the neighbor’s statement.

After Juror Number 8 was escorted from the jury room, he talked with his neighbor in the hallway. The court instructed the bailiff to tell the remaining jury members to take a recess from their deliberations during Juror Number 8’s absence from the jury room.

After completing .his conversation with his neighbor, Juror Number 8 reentered the courtroom outside of the presence of the other jurors. The trial judge asked Juror Number 8 to relate what the neighbor had told him. Juror Number 8 stated that the police had arrested the woman with whom he lived and had taken custody of her six-year-old boy. Juror Number 8 said that someone had called the police to report child abuse after the child had fallen off his bike. His neighbor told him that the boy had been slapped and had marks on him that looked like somebody burned him with a cigarette. Juror Number 8 said he was “sure it wasn’t her ... I can just say that she doesn’t smoke. [Her arrest] has been a mistake.” Juror Number 8 also stated:

Juror Number 8 further explained to the court that his friend told him that the police had been “real rough” with his girlfriend. The neighbor told him that the police “were pushing around and grabbing on her and pulling guns on her and pulling guns on him .., And she was crying, and they were shoving her around and put her in the car and stuff like that.” When asked what he would do if he were not on jury duty, Juror Number 8 explained that he would not post bail for her. Juror Number 8 then stated: “[Ljet’s say they want to talk to me, and they want to arrest me or something like that, then that would be a different story. But I just want to know if they want to ask me any questions. I am concerned about that.” (emphasis added).

Juror Number 8 also reported that his neighbor told him the police did not ask about him, but the police did not talk very much. Juror Number 8 informed the court that “there’s certainly a mistaken identity or something. You know, I am just not saying it because I know her. But I know that, you know, somehow she is probably falsely accused of something, and, you know, it is one of those mistakes.” (emphasis added).

Following this explanation, the district court held a conference with the prosecutor and defense counsel. The prosecutor requested that the juror be dismissed. The defense attorneys objected. After listening to both sides, the trial judge stated that he would excuse Juror Number 8 from the jury. The court informed counsel that it realized that the removal of the juror presented a “sensitive” issue which it had resolved only after “considerable deliberation.” The trial judge further explained that although he recognized that Juror Number 8 said he “could go about his work,” he did not ask the juror whether he could be fair and impartial because “it would be a rare juror who would stand up and say ‘under these circumstances, I can’t be fair and impartial.’ ” The court noted that the neighbor’s recitation of the facts involving the arrest of the juror’s girlfriend was contrary to Juror Number 8’s account. The court expressed its “very distinct, strong feeling ... that this juror was not forthcoming, which ties into his neighbor was not being forthcoming.” The court described Juror Number 8’s appearance as “somewhat nervous.” Juror Number 8 appeared “evasive, and his body language was such that I have a feeling he was shifting back and forth a bit.”

After reciting the events related by Juror Number 8, the court ruled as follows:

Before Juror Number 8 returned to the jury room, the district court received another note from the jury signed by eleven jurors. The note contained the following request:

After receiving the note, the court commented that the “discharge in no way bears upon this latest jury note. I will say to you that I had made the preliminary finding before the jury’s latest jury note came in, and I sought input from counsel. There was no input to in any way influence me to change my mind.”

On February 26, 1991, the district court supplemented its reasons for excusing Juror Number 8 in these words:

Juror Number 8 was discharged as a juror on the morning of February 21, 1991. After the remaining jurors returned from their lunch break, they deliberated for the rest of the afternoon. The jury continued its deliberations on Friday, February 22, 1991. The jury did not deliberate over the weekend or on the following Monday. They proceeded with deliberations on Tuesday, February 26, 1991. On February 26, 1991 at 4:10 p.m., the jury returned verdicts against Egbuniwe, Anyanwu, and Ari-shi.

DISCUSSION

I. Excusal of the Juror for Just Cause.

The appellants contend that the district court’s decision to excuse Juror Number 8 and to proceed with eleven jurors was reversible error. The appellants argue that the district court had a duty to inquire of the juror whether he was actually biased against the Government in this criminal matter because of the false arrest and rough treatment of his girlfriend by law enforcement officers.

We review a district court’s decision to excuse a juror after deliberations have commenced for abuse of discretion. United States v. Tabacca, 924 F.2d 906, 913 (9th Cir.1991). Under the abuse-of-discretion standard, we must affirm unless we are “left with the definite and firm conviction that the court committed a clear error of judgment in reaching its conclusion after weighing the relevant factors.” United States v. BNS, Inc., 858 F.2d 456, 464 (9th Cir.1988). We “cannot simply substitute our judgment for that of the district court.” Id.

In United States v. Dischner, 960 F.2d 870 (9th Cir.1992), we held that the district court did not abuse its discretion in excusing a juror who had broken her shoulder and would be unable to return to deliberations for over a week. Id. at 880 . We noted that “[ejxcusing a juror is generally appropriate when the trial is lengthy and waiting for the juror will result in a substantial or potentially uncertain delay.” Id. at 881 .

In Tabacca , the trial had lasted two and a half days. 924 F.2d at 913 . The government called three witnesses. Id. at 915 . After a day and a half of deliberations, the jury sent a note stating that it was deadlocked. Id. at 913 . The court excused the jury for a three-day weekend. Id. When the jury returned, the court learned that a juror could not come to the courthouse to participate in the jury’s deliberations because his wife had taken his car keys and he had no other means of transportation. Id. The jury returned a verdict approximately two hours after reconvening with eleven members. Id.

We held that the district court had abused its discretion because the brief two and a half day trial did not involve a substantial expenditure of resources. Id. at 915 . We also found it significant that the juror would be available the. following day. Id. We reasoned that an additional day’s delay in a trial of short duration would be “unlikely to induce dulled memories on the part of the jurors, even if they had taken a three-day weekend.” Id.

In this matter, the district court excused a juror after nine days of trial because it determined that the juror could no longer be fair and impartial after he was informed during jury deliberations of alleged police misconduct involving his girlfriend. Our research has not disclosed any other case in which a juror was excused during deliberations because he or she received extrajudicial information, unrelated to the criminal proceedings, which might prejudice the juror against a party. The closest case we have discovered involving the excusal of a juror who received extrajudicial information is United States v. Ruggiero, 928 F.2d 1289 (2nd Cir.), cert. denied, — U.S.-, 112 S.Ct. 372 , 116 L.Ed.2d 324 (1991). In Ruggiero , the district court received a note from the jury on the sixth day of deliberations which sought court guidance because one juror refused to vote. Id. at 1293 . Later that day, the court received a second note that stated that a juror refused to discuss the case. Id. The court then questioned Juror 9 in chambers. Id. The juror stated that the jury’s notes were inaccurate. Id. at 1294 . The juror explained he had discussed the case with his fellow jurors, but they were trying to persuade him to vote one way or the other. Id. He stated that he voted “on my conscious [sic].” Id. The court permitted Juror 9 to return to the jury room. Id.

Later that day, Juror 9 sent a note to the court which stated that the jury had talked about the fact that he could go to jail. Id. He also mentioned that his “residence is known” and he was concerned about his family. Id. at 1295 . The juror also wrote that he “simply can’t be persuated [sic] or forced to vote against my belief and conscience.” Id.

The court again called Juror 9 into chambers in the presence of counsel. Id. The court assured the juror that he would not go to jail and that no one knew where he lived. Id, The juror returned to the jury room. Id.

The next morning, the judge received a note from the jury indicating that although the jury had informally reached a unanimous decision, it could not return a verdict “due to the fears of one juror relating to alleged threats he received prior to deliberations.” Id.

Juror 9 was again questioned by the court. Id. The juror stated that he had encountered two men in his driveway the evening before the case was submitted to the jury. Id. He was not directly threatened. Id. The men told him that he was a juror in the Gene Gotti trial. Id. Juror 9 explained that he had not initially informed the court of the encounter because “he was not then frightened.” Id. The juror initially stated that he had questioned some of the testimony and he was not one hundred percent sure of the counts and the accusations. Id. at 1296 . He explained that “some aspects” of his vote were motivated by fear, but “not completely.” Id.

The court examined the juror further to determine unequivocally whether the juror was voting out of fear. Id. The juror stated that he was voting out of fear. Id. at 1297 . The Government moved for the dismissal of the juror pursuant to Rule 23(b). Juror 9 was excused for “good cause” over defense objection. Id.

On appeal, the Second Circuit upheld the trial court’s decision to excuse the juror. The court stated that it “would be rash indeed to second guess the conclusion of the experienced trial judge, based in large measure upon personal observations that cannot be captured on a paper record, that Juror No. 9 was disabled by fear from continuing to participate in the jury’s deliberations.” Id. at 1300 .

Based on his evaluation of the juror’s response to his questions, the trial judge in this matter concluded that the juror’s claim that he was not affected by reports of his girlfriend’s physical abuse and false arrest was not truthful. The Supreme Court has recognized that the “determination of impartiality, in which demeanor plays such an important part, is- particularly within the province of the trial judge.” Ristaino v. Ross, 424 U.S. 589, 595 , 96 S.Ct. 1017, 1020 , 47 L.Ed.2d 258 (1976); see also Patton v. Yount, 467 U.S. 1025, 1038 , 104 S.Ct. 2885, 2892 , 81 L.Ed.2d 847 (1984) (holding that trial court’s determination of prospective juror’s credibility is largely based on demeanor and is entitled to special deference).

The appellants assert that the court erred as a matter of law in failing to ask the juror if he could be fair and impartial. We disagree. A juror’s assurance that he or she can render a fair and impartial verdict is not dispositive. Murphy v. Florida, 421 U.S. 794, 800 , 95 S.Ct. 2031, 2036 , 44 L.Ed.2d 589 (1975). A trial judge is required to make an independent assessment of a juror’s ability to render a fair and impartial verdict. See United States v. Ramos, 861 F.2d 461, 464-66 (6th Cir 1988); cert. denied, 489 U.S. 1071 , 109 S.Ct. 1353 , 103 L.Ed.2d 820 (1989) (affirming the district court’s decision to excuse a juror despite the juror’s assurances that his wife had not disclosed the substance of her conversation with the defendant and his wife); United States v. Gabay, 923 F.2d 1536, 1542-43 (11th Cir.1991) (district court did not err in removing a juror accused of discussing the defendant’s guilt before deliberations began even though juror denied such discussions had occurred).

The appellants further assert that the district court’s reasons for excusing Juror Number 8 are not supported by the record. They contend that Juror Number 8’s answers demonstrated he was indifferent to the fate of his girlfriend, and not that he was biased against law enforcement.

While some of Juror Number 8’s statements expressed his indifference to the fate of his girlfriend, the district court’s finding that it had “serious doubts on [Juror Number 8’s] ability to concentrate on the deliberations in this case and/or on his ability to be a fair and impartial juror” is supported by the record. Juror Number 8 expressed a concern that the police might want to arrest him. Juror Number 8’s girlfriend was charged with a serious offense. Juror Number 8 stated that his neighbor told him that the police had physically mistreated his girlfriend and that he believed the charges against her were false. These facts, combined with Juror Number 8’s “defensive demeanor and failure to be forthcoming,” constituted just cause for excusing Juror Number 8 because he might not be able to be fair to both parties.

The appellants argue that the discharge of the juror was prejudicial because the jury continued deliberating while the court questioned Juror Number 8. They also assert that the district court’s decision to dismiss Juror Number 8 was based in part on the jury’s note accusing Juror Number 8 of being nonobjective and threatening.

The record does not support these contentions. The jury deliberated for several hours before Juror Number 8 was excused. After Juror Number 8’s removal, the jury continued to deliberate for an additional two and a half days.

The record shows that the court instructed the remaining jurors to take recess from their deliberations while Juror Number 8 was outside of their presence. There is no evidence that would support an inference that the jurors continued their deliberations while Juror Number 8 was being questioned by the court.

Appellants have also failed to demonstrate that the district court’s decision to excuse the juror was influenced by the jury’s last note regarding Juror Number 8’s conduct during deliberations. The trial judge expressed his intention to excuse Juror Number 8 before receiving the note from the jurors. At the time Juror Number 8 was excused, the district court explained that the jury’s note had not influenced its decision to excuse Juror Number 8. In its subsequent comments, the court observed that the jury’s note concerning Juror Number 8’s behavior confirmed its conclusion that the juror was biased. The court stressed again, however, that the note had no bearing on its Rule 23(b) decision.

The district court’s decision to proceed with an eleven-person jury promotes the underlying purpose of Rule 23(b). This case involved 9 days of trial, over 1800 pages of testimony, approximately 25 witnesses, and over 120 exhibits. A retrial in this matter would have involved a substantial expenditure of tax dollars and the consumption of judicial resources. The district court did not abuse its discretion in excusing Juror Number 8 for just cause based on the fact that he received information that appeared to bias him against law enforcement in this criminal case.

II. Amount of Cocaine Attributable to Egbuniwe.

Egbuniwe asserts that the district court clearly erred in finding that he was accountable for over 1000 grams of heroin for purposes of sentencing. Egbuniwe was convicted of the following counts: conspiracy to possess with the intent to distribute over 1000 grams of heroin, and possession with the intent to distribute 433.8 grams of heroin. Egbuniwe asserts that his sentence is inconsistent with that received by his co-conspirator Anyanwu. In sentencing Anyanwu, the district court took into consideration only the amount of heroin actually possessed by Anyanwu because it found that Anyanwu was unaware of the 433 grams of heroin smuggled by Arum and Irokameje. Egbuniwe argues that he should not be held responsible for the 711 grams of heroin possessed by Anyanwu.

We review a district court’s interpretation of the sentencing guidelines de novo and its factual findings for clear error. United States v. Wilson, 900 F.2d 1350, 1355 (9th Cir.1990). The amount of contraband attributable to a defendant is a matter for the district court to determine at sentencing. United States v. Sotelo-Rivera, 931 F.2d 1317, 1319 (9th Cir.1991), cert. denied, - U.S. -, 112 S.Ct. 1186 , 117 L.Ed.2d 428 (1992). The district court is not bound by the jury’s determination of the amount involved. United States v. Moreno, 899 F.2d 465, 473 (6th Cir.1990), cert. denied, - U.S. -, 112 S.Ct. 1504 , 117 L.Ed.2d 643 (1992). A sentencing court must determine the amount of contraband by a preponderance of the evidence. United States v. Restrepo, 946 F.2d 654, 661 (9th Cir.1991) (en banc), cert. denied, - U.S. -, 112 S.Ct. 1564 , 118 L.Ed.2d 211 (1992).

The fact that the district court exercised leniency in sentencing Anyanwu did not preclude it from finding that Egbuniwe was accountable for the amount of heroin possessed by other members of the conspiracy. Cf. United States v. Carpenter, 914 F.2d 1131, 1135-36 (9th Cir.1990) (holding that the Sentencing Guidelines do not prohibit co-defendants participating in the same crime from receiving inconsistent sentences). A defendant who participates in a conspiracy may be held responsible for all substantive offenses committed by his co-conspirators in furtherance of the conspiracy, even if he did not directly participate in their commission. United States v. Vasquez, 858 F.2d 1387, 1393 (9th Cir.1988), cert. denied, 488 U.S. 1034 , 109 S.Ct. 847 , 102 L.Ed.2d 978 (1989).

At Egbuniwe’s sentencing hearing, the district court found that he was accountable for the heroin possessed by other members of the conspiracy. The record demonstrates that the district court’s conclusion is not clearly erroneous. Egbuniwe was present at a lunch meeting at his apartment when Ijemba, Arum, and Irokameje discussed the plan to smuggle heroin from Nigeria. Egbuniwe’s phone records indicated that several calls were made to individuals in Detroit who had agreed to purchase the heroin. Egbuniwe telephoned Arum and Irokameje’s motel room immediately after they asked Ijemba to pick up the heroin which they had smuggled from Nigeria. During this telephone conversation, Egbuniwe asked Arum why he had not contacted Egbuniwe the previous day. Egbuniwe then asked for Arishi’s room number. Arishi had traveled with Anyan-wu to Nigeria, bought their plane tickets, and arranged for Anyanwu to swallow heroin in Nigeria.

When he came to the motel room to pick up the heroin, Egbuniwe warned Arum and Irokameje to “get away from this place.” Egbuniwe told them that Ijemba wanted “this thing to be removed from here.” Shortly after his arrest, Egbuniwe’s beeper was activated. The phone number of Ijem-ba’s business appeared on the display. The paging company records demonstrated the Ijemba had rented the pager. Moreover, Egbuniwe’s phone number was in Arishi’s phone book.

The above evidence demonstrates that the district court did not clearly err in finding that, by a preponderance of the evidence, Egbuniwe was a knowing participant in a conspiracy to distribute over 1000 grams of heroin.

AFFIRMED.