BUTZNER, Senior Circuit Judge:
Wayne Porter, Thomas Bell, Lewis Barrentine, Earl Jolly, and James Hand appeal judgments convicting them of violating laws pertaining to the importation and distribution of drugs. They were indicted with 34 other defendants in a 45-count indictment. We affirm on all but several counts.
Porter was charged in 28 counts, including 5 charges of conspiracy in violation of 21 U.S.C. § 846 and one charge of engaging in a continuing criminal enterprise in violation of 21 U.S.C. § 848. The remaining charges included counts of possession with intent to distribute controlled substances in violation of 21 U.S.C. § 841, use of a communication facility in the commission of a drug felony in violation of 21 U.S.C. § 843, traveling in interstate commerce to carry on illegal drug activity, 18 U.S.C. § 1952, and aiding and abetting. Bell was charged in 15 counts, and Barren-tine, Jolly, and Hand were charged in 7 counts. Each was charged in count 1 with conspiring with Porter and several counts of possession with intent to distribute.
Recognizing the size and difficulty of a single trial and despite its conclusion that all defendants were properly joined, the district court divided the case into three trials. The appellants were tried with two other defendants in the first trial. Testimony disclosed five separate occasions on which Porter, the ringleader, and others went to Georgia or Florida to bring marijuana imported from Colombia and sometimes other drugs to Wilkes County, North Carolina, for distribution.
After a 10-day trial, a jury convicted Porter of 16 counts, including all five conspiracies and the continuing criminal enterprise count. Bell, Barrentine, Jolly, and Hand each were convicted of four counts, including the count 1 conspiracy and three counts of possession with intent to distribute.1 William Peterson was acquitted on the only charge against him. Terry Porter was acquitted of one of the three charges against her, and no verdict was returned on the other two.
I
Hand, Barrentine, Jolly, and Bell argue that the district court erred in denying their motions to sever their trial from that of Porter. The charges against them in counts 1-7 dealt with the occasion that Porter obtained marijuana and methaqualone in Florida using a boat called the “Frances Louise.” Porter was tried on those counts and an additional 12 counts in [972]*972which Hand, Barrentine, Jolly, and Bell were not named. They contend that joinder was improper under Fed.R.Crim.P. 8 because they suffered prejudice due to the admission of evidence unrelated to their charges and inadmissible against them in a separate trial.
We find no error. Rule 8(b) permits joinder of defendants if “they are alleged to have participated in the same act or transaction or in the same series of acts or transactions constituting an offense or offenses.” Separate acts constituting separate offenses are sufficiently related to be within the same series if they arise out of a common plan or scheme. United States v. Guerrero, 756 F.2d 1342, 1345 (9th Cir. 1984). There must be a series of acts unified by some substantial identity of facts or participants. United States v. Dennis, 645 F.2d 517, 520 (5th Cir.1981). That was clearly the case here. All those indicted were alleged to have participated in a drug importation and distribution scheme run by Porter. Because the indictment charged Porter with engaging in a continuing enterprise based on a series of crimes, including those involving the other appellants, joinder was proper under Rule 8(b).
Nor did the trial court abuse its discretion under Fed.R.Crim.P. 14 in denying a severance. A defendant must show prejudice in order for the court’s ruling to constitute an abuse of discretion. United States v. Phillips, 664 F.2d 971, 1016-17 (5th Cir.1981). No prejudice exists if the jury could make individual guilt determinations by following the court’s cautionary instructions, appraising the independent evidence against each defendant. Convictions should be sustained if it may be inferred from the verdicts that the jury meticulously sifted the evidence. Phillips, 664 F.2d at 1017.
Hand, Barrentine, Jolly, and Bell have shown no prejudice. The judge repeatedly instructed the jury that the testimony was to be considered against a particular defendant or defendants. The verdict reflects that the jury carefully considered the evidence against each defendant. It acquitted Peterson of the only charge against him and acquitted Terry Porter of one of three charges against her.
II
The appellants argue that the district court also erred in its instruction defining reasonable doubt. They contend that the court should not have attempted any definition, that the specific definition given was confusing, and that it shifted the burden of proof, depriving them of due process of law.
This court has urged trial courts to avoid defining reasonable doubt unless requested to do so by the jury, because of the risk that the definition will create confusion and impermissibly lessen the required burden of proof. See United States v. Love, 767 F.2d 1052, 1060 (4th Cir.1985). Attempts at defining reasonable doubt in a charge do not constitute reversible error per se, however. United States v. Moss, 756 F.2d 329, 333 (4th Cir.1985). To determine whether an instruction on reasonable doubt is sufficiently prejudicial to require reversal, we must look to the entire charge and its context. If the charge correctly conveys the concept of reasonable doubt, reversal is not required. Moss, 756 F.2d at 333-34. Even if the definition of reasonable doubt tends to lessen the government’s burden of proof, the other instructions may neutralize the possible prejudicial effect of the challenged instruction. Moss, 756 F.2d at 334.
The district court charged as follows:
As I have said many times, the government has the burden of proving the defendant guilty beyond a reasonable doubt. Some of you may have served as jurors in civil cases where you were told it was only necessary to prove that a fact is more likely true than not true. In criminal cases, the government’s proof must be more powerful than that. It must be beyond a reasonable doubt. Proof beyond a reasonable doubt is proof that leaves you firmly convinced of the defendant’s guilt. There are very few things in this world that we know with [973]*973absolute certainty, and in criminal cases the law does not require proof that overcomes every possible doubt.
If, based on your consideration of the . evidence, you are firmly convinced the defendant was guilty of the crimes charged, any particular defendant, you must find that particular defendant guilty. If, on the other hand, you think there is a real possibility he’s not guilty, you must give him the benefit of the doubt and find him not guilty.
The appellants object to the final sentence, arguing that it is confusing and shifts the burden of proof to them to prove that there was a real possibility that they were not guilty.
More than a century ago the Supreme Court observed: “Attempts to explain the term ‘reasonable doubt’ do not usually result in making it any clearer to the minds of the jury.” Miles v. United States, 103 U.S. (13 Otto) 304, 312, 26 L.Ed. 481 (1881). Nearly 75 years later, the Court deemed it advisable to reiterate its note of caution. See Holland v. United States, 348 U.S. 121, 140, 75 S.Ct. 127, 138, 99 L.Ed. 150 (1954). In Moss, 756 F.2d at 333, Judge Ervin listed the many courts that have paid heed to the Supreme Court’s admonition. The district court’s instruction in this case illustrates the confusion that is engendered by attempting to define a reasonable doubt in terms of a “real possibility” that the accused is not guilty. The district court did not explain the difference that it perceived between a “possibility” and a “real possibility.” It failed to tell the jury that the accused did not have the burden of showing a “real possibility” of innocence. Implying the evidence must show a real possibility of innocence to justify acquittal trenches on the principle that a defendant is presumed to be innocent. If the court believed that the jury could understand its concept of a “real possibility” and allocate the burden of proof on this issue, there was no reason for it to question the jury’s ability to understand the prosecution’s obligation to prove the charges beyond a reasonable doubt.
Nevertheless, we conclude that the district court’s error does not warrant reversal. Contrary to the appellants’ protests, the instruction did not shift the burden of proof on the question of a real possibility. Instead it failed to allocate the burden. Other instructions, however, compensated for this omission.
The court properly instructed the jury: The law presumes a defendant to be innocent, and the presumption of innocence alone is sufficient to acquit a defendant, unless the jury is satisfied beyond a reasonable doubt of the defendant’s guilt after careful and impartial consideration of the evidence introduced at trial.
A defendant has no obligation to establish his innocence. The burden is always upon the prosecution to prove guilt beyond a reasonable doubt, and this burden never shifts to the defendant. If the jury, after careful and impartial consideration of all the evidence, has a reasonable doubt that a defendant was guilty of the charge under consideration, you must find that defendant not guilty of that charge.
If, on the other hand, the jury finds that the evidence is sufficient to overcome the presumption of innocence and to convince you beyond a reasonable doubt of the guilt of the defendant of the charge under consideration, it must find the defendant guilty of that charge.
The instructions taken as a whole properly described the prosecution’s burden and the protection the law affords the accused. Therefore, the error, which introduced the unnecessary concepts of being “firmly convinced” of guilt and a “real possibility” of innocence, did not affect the substantial rights of the accused. It should be disregarded. See Fed.R.Crim.P. 52.
We find no error in the district court’s refusal to provide appellants with written copies of its intended instructions before charging the jury. The court allowed the parties to submit their requested instructions. At a conference before closing arguments, the court informed counsel of its proposed action on most of the requested instructions, and it reviewed orally [974]*974many of the instructions it would give. It also reminded counsel that they would be given an opportunity to object and to propose any additional instructions after it had completed its charge to the jury. The court sufficiently complied with Fed.R. Crim.P. 30. The appellants’ complaint about the instructions pertaining to an accomplice’s testimony discloses no error.
Ill
The appellants contend that the district court erred in allowing a part of the plea agreement of a witness, Rodney Foster, to be read to the jury and admitted into evidence. The objectionable portion stated that Foster agreed to provide truthful information about criminal activity within his knowledge and further stated “[t]his information may be verified by polygraph or any other method which the United States shall choose to employ.” The appellants contend that admission of the polygraph provision of the plea agreement constituted impermissible bolstering of Foster’s credibility and therefore was reversible error.
Evidence of a plea agreement containing a provision that the government’s witness has agreed to take a polygraph test to verify trial testimony constitutes impermissible bolstering of the witness’s credibility. United States v. Hilton, 772 F.2d 783, 786 (11th Cir.1985). We conclude, however, that the error in admitting the reference to a polygraph was harmless beyond a reasonable doubt. We note first that the government made no further use of the plea agreement or the polygraph. At no other time did it attempt to link Foster’s credibility to the plea agreement. In this respect the case differs from Hilton where the prosecutor contended in final argument that crucial witnesses were credible because they had agreed to take polygraph exams. 772 F.2d at 785-86 and n. 1.
The evidence of guilt was sufficient without Foster’s testimony. Additionally, Foster’s evidence was corroborated. Consequently, the reference to a polygraph test does not warrant reversal. See United States v. Brevard, 739 F.2d 180, 182 (4th Cir.1984); United States v. Morrow, 731 F.2d 233, 238 (4th Cir.1984).
The appellants’ argument that admission of Foster’s plea agreement also bolstered the credibility of other witnesses who had plea bargained is too tenuous to constitute reversible error. The government introduced no evidence about other polygraph tests.
IV
The appellants challenge the admission of photographs which were seized in January 1981 from the “Frances Louise” by customs officers in Charleston, South Carolina. The photographs included pictures of some of the alleged conspirators standing together and of some of them outside of Bell’s house. The appellants argue that the photographs should not have been admitted because they were not properly authenticated and they were not introduced as substantive evidence or to illustrate testimony.
We find no error. The government offered the photographs to support the inference that the conspirators photographed together most likely knew each other prior to January 1981. The officer who seized the “Frances Louise” testified that the photographs were found on the boat. The chain of custody after the seizure was sufficiently established by the testimony of officers who received the photographs after they were seized. A witness who testified concerning the roles of Porter and Bell in the crimes identified people and some of the places in the photographs. The photographs belonged to the conspirators, and there was no reason to suspect that they were not what they were purported to be.
V
We find no error in the admission of Porter's and Barrentine’s telephone toll records. The initiating and receiving telephones were sufficiently identified. Discrepancies the appellants detected in some of the toll records raised questions about the weight of the evidence but did not [975]*975render it inadmissible. Nor did the court abuse its discretion in admitting the charts which summarized the telephone calls. Summary charts may be admitted if they are based upon and fairly represent competent evidence already before the jury. United States v. Keltner, 675 F.2d 602, 605-06 (4th Cir.1982). See also United States v. Drougas, 748 F.2d 8, 25-26 (1st Cir.1984) (chart summarizing over 100 telephone calls placed during conspiracy properly admitted). The charts did not add any evidence; nor do the appellants suggest that the charts inaccurately represent the toll records. Any potential prejudice from the manner in which some names were highlighted on the chart was cured by the court’s instruction that the charts merely summarized records already in evidence and that the arrangement of the names had nothing to do with any defendant’s culpability.
VI
Porter contends that count 16 charging him with conspiracy to possess marijuana and cocaine in June, July, or August 1981 to September of 1981, should have been dismissed by the court because venue in the Western District of North Carolina was not proved.
The government must show by a preponderance of the evidence that the trial is in the same district as part of the criminal offense. United States v. White, 611 F.2d 531, 534-36 (5th Cir.1980). Because, as it concedes, the government did not show that any overt act alleged in count 16 was committed in the Western District of North Carolina, Porter’s conviction must be reversed.
Porter also challenges his convictions of counts 17 and 25, each charging him with traveling in interstate commerce for the purpose of carrying on an illegal drug activity in violation of 18 U.S.C. § 1952. The evidence showed that on both occasions Porter traveled to Georgia for the purpose of acquiring drugs. He obtained none, however, because the marijuana boats did not show up. Intent alone does not satisfy the requirements of 18 U.S.C. § 1952. The government must prove that Porter performed or attempted to perform an act in furtherance of illegal activity after he arrived in Georgia. United States v. Becton, 751 F.2d 250, 255 (8th Cir.1984). Because this was not shown, Porter’s convictions under counts 17 and 25 cannot be sustained.
Counts 27 and 28 of the indictment charged Porter and his wife, Terry, with using a telephone to facilitate the commission of a felony in violation of 21 U.S.C. § 843. Before the case was submitted to the jury, the district court dismissed the charges against Terry for lack of evidence. Porter contends that exactly the same evidence applied to him and that the evidence was insufficient to sustain his convictions.
The government presented no evidence about the substance of calls placed by Porter from Lyons, Georgia, to Porter’s number in Wilkes County. No connection was made between any of the calls and any illegal drug transaction by Porter. Because we conclude that no substantial evidence supports the jury’s finding of guilt beyond a reasonable doubt, Porter’s convictions in counts 27 and 28 must be reversed. See United States v. Stockton, 788 F.2d 210, 218 (4th Cir.1986).
VII
The district court permitted a drug enforcement agent to testify concerning a Florida investigation involving Porter which took place between May and July 1982. The agent testified that on July 22, 1982, he was executing a search warrant at Porter’s residence in Charlotte, North Carolina, when Porter called from Tennessee and the agent answered the phone. He told Porter that a federal grand jury in Florida had indicted him for importation and possession and that he had a warrant for Porter’s arrest. After the agent advised him to turn himself in, Porter hung up. Porter remained a fugitive until he surrendered in November 1983, more than a year later. He ultimately pled guilty to importation, possession with intent to distribute, and use of a communication facility [976]*976in furtherance of a drug felony in the Middle District of Florida.
The court instructed the jury that, if it believed the agent’s testimony, it could consider the fact that Porter did not turn himself in after he was told there was a warrant for his arrest as evidence that he knew he was guilty of the crime for which he was being tried.
Porter contends that the court erred in giving the instruction on these facts. He argues that his flight after his conversation with the agent could at most be evidence that he knew of his guilt of the crimes charged in the Middle District of Florida.
The government contends that the evidence of flight was relevant to the charge of engaging in a continuing criminal enterprise in violation of 21 U.S.C. § 848 as charged in count 34 of the present indictment. Because the evidence was relevant, the government argues that the instruction was proper.
The chain of inferences leading from evidence of flight to consciousness of guilt must lead to consciousness of guilt of the crime charged. United States v. Schepp, 746 F.2d 406, 409-10 (8th Cir.1984). In United States v. Beahm, 664 F.2d 414, 419-20 (4th Cir.1981), we cautioned that the inference of consciousness of guilt “would be completely unfounded where a defendant flees after ‘commencement of an investigation’ unrelated to the crime charged, or of which the defendant was unaware.” Accord United States v. Foutz, 540 F.2d 733, 739-40 (4th Cir.1976). In United States v. Hawkes, 753 F.2d 355, 358-59 (4th Cir.1985), we reversed because the trial court instructed the jury about intentional flight without adequate evidentiary support to show that the defendant had fled.
The admission of the agent’s testimony and the court’s instruction concerning flight do not transgress any of these principles. The crime charged in the Florida indictment was the last of the series of crimes related to drugs on which the government relied to prove that Porter engaged in a criminal continuing enterprise as charged in count 34 of the present indictment. Porter knew he had illegally imported and possessed drugs on many occasions. He did not know, however, precisely which violations were the subject of the prosecution in Florida. The jury reasonably could find that he became a fugitive to escape any prosecution for his numerous violations of the drug laws, which ultimately led to his present indictment for engaging in a continuing criminal enterprise. Therefore, the instruction was proper.
VIII
Barrentine argues that the district court erroneously admitted inculpatory statements he made to a United States customs officer in several telephone conversations he initiated. He contends that these statements were made pursuant to plea negotiations and therefore were inadmissible under Fed.R.Crim.P. 11(e)(6).
During his investigation following the seizure of Barrentine’s boat, the “Frances Louise,” the officer received several telephone calls from Barrentine. In the first conversation, Barrentine claimed that purchasing the boat was his only participation in the importation of drugs. Barrentine offered to participate with the officer to catch Porter. The officer explained that he could not make a deal but offered to discuss Barrentine’s suggestion with the case agent. During ensuing phone conversations Barrentine explained what he hoped to gain from any deal: retention of a home in which he had invested insurance money, relocation because he feared for his safety, and avoidance of prosecution. Eleven days after the first conversation, Barrentine called again and the officer responded that no deal could be worked out then. He encouraged Barrentine to contact him again because something might be worked out later. The officer had no further contact with Barrentine.
Rule 11(e)(6) provides that statements made in connection with, and relevant to, offers to plead guilty are not admissible in a criminal trial against the person who made the plea offer. “Plea bargaining implies an offer to plead guilty [977]*977upon condition.” United States v. Levy, 578 F.2d 896, 901 (2d Cir.1978). Plea negotiations, in order to be inadmissible, must be made in negotiations with a government attorney or with that attorney’s express authority. Fed.R.Crim.P. 11(e)(6)(D); Rachlin v. United States, 723 F.2d 1373, 1376 (8th Cir.1983).
We conclude that the rule does not apply to Barrentine’s statements because they were not made pursuant to plea negotiations. No charges had been brought against Barrentine when he contacted the officer. He did not offer to plead guilty but, in fact, expressed the wish not to be prosecuted in exchange for working with the officer to get more information about Porter’s drug operation. The officer explicitly told Barrentine that he had no authority to make such a deal. Barrentine made his statements as an informant, hopeful of getting a break.
Barrentine also claims that the statements were improperly admitted because the government did not timely disclose them pursuant to Fed.R.Crim.P. 16.
Defense counsel received the officer’s report six days before the beginning of the trial. The report was four pages long. The government turned it over as soon as it received it. The officer testified late the fourth day of trial. Barrentine has shown no prejudice from receiving the report when he did.
IX
Hand objects to the admission into evidence of several documents purportedly showing that he was employed by Houdaille Industries in Jacksonville, Florida, at the time of the “Frances Louise” incident. An employee hiring card, a termination slip, and two forms from the Florida Bureau of Unemployment Compensation were introduced through the testimony of a security officer of Houdaille Industries. Hand argues that these records were improperly admitted under Fed.R.Evid. 803(6), the business records exception to the hearsay rule, because they were introduced without proper authentication. The security officer was not a qualified witness under the terms of Rule 803(6). He simply had access to the files of closed companies of Houdaille Industries. He was not the custodian of records. He did not work in the personnel department where such records were made, and he did not know the record keeping requirements of the company. He could testify only that he knew that the employee hiring cards were used.
We find, however, that the error was harmless in light of the evidence against Hand. See Williams v. Zahradnick, 632 F.2d 353, 360-65 (4th Cir.1980). The business records corroborated the government’s evidence that Hand provided access to the offloading site. Proof of that act was not necessary in order to convict him. He guided trucks carrying marijuana to a rendezvous at his farmhouse with other conspirators. Then, to elude Florida police, he led the conspirators over back roads to Georgia. The evidence was sufficient to enable a rational trier of fact to find that Hand was guilty. We conclude that the error did not influence the jury’s verdict.
X
Porter makes several assignments of error concerning his conviction under count 34 of engaging in a continuing criminal enterprise. He contends that the court erroneously admitted evidence of incidents that occurred before the date alleged in the indictment, creating an impermissible variance between the indictment and the proof offered at trial. He also contends that the court erred in admitting evidence of a Florida drug offense that extended beyond the date in the indictment. He argues that the Florida offense was improperly offered as one of the predicate offenses for the continuing criminal enterprise. Finally, he contends that the court improperly sentenced him for the conspiracy convictions in addition to his sentence for the continuing criminal enterprise conviction.
Count 34 of the indictment alleged that “from on or about September or October 1980 and continuing thereafter and in-[978]*978eluding June 1982” Porter engaged in a continuing criminal enterprise. The government offered evidence of two drug transactions that had occurred prior to September 1980. The first occurred in the spring of 1980 and the second in August of 1980. Porter was not indicted for either of these incidents. The trial court admitted the testimony under Fed.R. of Evid. 404(b) as showing “motive, knowledge, and state of mind.” We find no abuse of discretion.
The Florida guilty plea was admitted for the purpose of meeting the series element under 21 U.S.C. § 848(b)(2) of the continuing criminal enterprise charge. We find no error. Although Porter actually pled guilty some time after November 1983, the events that led to the Florida charges occurred between May and July 1982. Thus proof of those events extended only one month beyond the date alleged in the indictment. The district court noted that the variance between the indictment and proof was slight. The government put Porter on notice through a bill of particulars that it would include those events in its proof for count 34. Finally, Porter’s convictions in counts 2, 4, 7, 8, 26, and 29 more than sufficed to meet the § 848(b)(2) series element. See United States v. Sterling, 742 F.2d 521, 526-27 (9th Cir.1984).
We agree with Porter, however, that the court erred in sentencing him for the conspiracy convictions. The court sentenced Porter to 75 years on the continuing criminal enterprise conviction. It imposed concurrent sentences on the conspiracy convictions. Congress did not intend that an individual be punished under both § 846 (conspiracy) and § 848 (continuing criminal enterprise). United States v. Garrett, 471 U.S. 773, 794, 105 S.Ct. 2407, 2419-20, 85 L.Ed.2d 764 (1985); Jeffers v. United States, 432 U.S. 137, 154-58, 97 S.Ct. 2207, 2218-20, 53 L.Ed.2d 168 (1977) (plurality opinion). Therefore, Porter’s sentences for his conspiracy convictions, counts 1, 18, 19, and 24, must be set aside. In Part VI we reversed the conviction of conspiracy charged in count 16.
Porter contends that he was prejudiced by a variance between the indictment that charged five conspiracies and the evidence, which, he asserts, showed only one conspiracy. It is, however, unnecessary to decide this issue. There are sufficient other offenses to establish the series required for § 848(b)(2). Also, our action in vacating the sentences imposed on the conspiracy counts makes the number of conspiracies immaterial.
XI
The case is remanded with directions that Porter's convictions under counts 16, 17, 25, 27, and 28 be reversed, and his sentences under counts 1, 18, 19, and 24 be set aside. In all other respects, the judgments of the district court are affirmed.