Dewayne Ervin here appeals his conviction and sentence on charges of drug trafficking and illegal possession of firearms. He contends that the district court committed prejudicial error in the denial of a motion to suppress evidence, the admission of a federal agent’s expert testimony, the dismissal of an absent juror, and the determination of drug quantities for purposes of sentencing. Finding none of these contentions persuasive, we shall affirm the challenged judgment.
*633i
Evidence leading to Mr. Ervin’s indictment was gathered in three separate searches. The first occurred during a traffic stop in Madison County, Florida, in July of 1999. Officer Doug Haskell of the Madison County Sheriffs Department allegedly observed a car traveling at about 60 miles per hour in a 70 mile per hour zone — a speed that Officer Haskell said he considered “unusual[ly] slow.” Haskell decided to follow the car, after which, he later testified, he saw it cross the white line into the emergency lane two or three times. Haskell then turned on the video camera mounted in his patrol car. After seeing the car touch the white line again, he directed the driver to pull over.
The officer approached the car and asked the driver, Yuseff Woodruff, for his driver’s license. Mr. Woodruff produced two licenses belonging to other drivers before surrendering his own license, which proved to have been suspended. Wood-ruffs “hands were shaking extremely bad,” according to Haskell. Woodruff told Haskell that he and his passenger, Mr. Ervin, had got lost on their way to Miami to attend a concert. When Haskell questioned Ervin, however, Ervin said that he and Woodruff were going to Miami for “no special reason.” Woodruff told Haskell that the car had been rented by Ervin’s grandfather.
Before he was placed under arrest for driving with a suspended license, Woodruff consented to a search of the vehicle. The search uncovered almost $25,000, wrapped in $1000 bundles, between the spare tire and the underside of the car. This money was seized. A pat-down of Ervin uncovered an additional $2000 cash in Ervin’s pants pockets. The $2000 was not seized.
The second search occurred on May 19, 2000. After an informant, Robert Fears, told Chattanooga police that he had purchased cocaine from Mr. Ervin at an auto paint and body shop called “Kandy Kustoms,” the police set up a controlled buy. Under police supervision, Fears met Ervin at Kandy Kustoms and purchased a kilogram of cocaine. Fears told police that he had observed another drug transaction while at the shop, and that there were more drugs on the premises. On the strength of all this, Officer Gerald Dossett of the Chattanooga Police Department obtained a warrant to search the Kandy Kustoms premises.
While awaiting the search warrant, police approached Kandy Kustoms and reportedly saw two men enter the building from the porch, close the door, and lock it. The officers testified later that they heard people running around and yelling inside the shop. Deciding that they needed to secure the premises, the officers made a forced entry, apprehended Mr. Ervin, Mr. Woodruff, and a third man, and then performed a protective “sweep” to ascertain that no one else was present. Marijuana and a stack of cash were in plain view, as was a black bag in the middle of the floor. The officers did not search the bag before the arrival of the warrant.
When Officer Dossett arrived with the search warrant, police examined the black bag and found it contained about five kilograms of cocaine. The officers also discovered about $27,000 in cash, some marijuana, and a number of cellular telephones.
The third search, which occurred on the same night as the Kandy Kustoms search, also resulted from information provided by Mr. Fears. Fears told police that he had purchased cocaine from Mr. Ervin at Ervin’s residence two days earlier. A substantial quantity of cocaine was said to have remained at the residence. A search of the residence, conducted pursuant to another warrant, resulted in the discovery of cocaine, marijuana, firearms, and ammunition.
*634A grand jury indicted Mr. Ervin on charges of conspiracy to distribute at least five kilograms of cocaine powder and at least 50 grams of cocaine base; distribution of at least 50 grams of cocaine base; distribution of at least 500 grams of cocaine powder; and illegal possession of firearms. Ervin moved to suppress the evidence seized in the three searches. After a hearing, a magistrate judge recommended that the motion be denied. The district court adopted this recommendation over Ervin’s objections.
Mr. Ervin’s case went to trial before a jury. The evidence sought to be suppressed by Mr. Ervin was received by the court, leading to one of the assignments of error on appeal. Also challenged on appeal is the denial of a motion to exclude a federal agent’s expert testimony relating to general practices within the drug trade, including sources of cocaine, forms of distribution, pricing, and jargon used by drug dealers and purchasers.
In addition to its rulings on the admissibility of evidence, the district court made two other decisions that we are asked to review. First, the court declined to instruct the jury that it must determine the exact quantity of drugs attributable to Mr. Ervin, as well as the exact number of conspirators involved in the drug conspiracy. Second, the court dismissed a juror who called in sick on the second day of jury deliberations. She was apparently the “only minority member on the jury.” Before dismissing the juror, the court attempted to contact her and determine when she might be able to resume service. The juror did not answer the phone, however, and did not return the court’s calls until noon or thereabouts. The court replaced the sick juror with an alternate at 10:41 a.m., whereupon the jury resumed its deliberations. When the juror finally called back, she explained that she was “in and out” because of medicine that made her drowsy. The juror indicated that she might have been available that afternoon.
The jury convicted Mr. Ervin on each count of the indictment. It specifically found that he was responsible for the drug quantities charged in the indictment.
At sentencing, the district court adopted the drug quantity calculations memorialized by a probation officer in a presentence report. The court declined a request by Mr. Ervin to apply the “reasonable doubt” standard in this connection. The court sentenced Ervin to imprisonment for life on his convictions for conspiracy and distribution of cocaine base, 480 months on his conviction for distribution of cocaine powder, and 120 months on his conviction for possessing firearms, the sentences to run concurrently. This appeal followed.
II
A
Mr. Ervin argues that the district court should have suppressed all evidence obtained during the Florida traffic stop. In the first place, he says, Officer Haskell did not have a legal basis to stop the vehicle in which Ervin was traveling. Driving 10 miles per hour below the posted limit is not an inherently suspicious activity, Ervin submits, and the traffic violations that Haskell claims to have observed were not captured by the video camera.1 The real reason for the stop, Ervin suggests, *635was that he and Woodruff were young black men driving an expensive car.
Unfortunately for Mr. Ervin, credibility determinations are the province of the district court. We see no basis for disturbing the determination that was made here. The magistrate judge credited Officer Haskell’s testimony that the car crossed the white line two or three times. Mr. Ervin has pointed to contrary testimony— which the magistrate judge disbelieved— but he has not shown the magistrate judge’s factual finding to be clearly erroneous.
Crossing the white line violates Florida’s careless driving statute. See Fla. St. Ann. § 316.1925. Accepting Officer Haskell’s testimony as true, therefore, we must reject the claim that Haskell lacked a reasonable basis to stop the vehicle. See United States v. Ferguson, 8 F.3d 385, 391 (6th Cir.1993) (en banc), cert. denied, 513 U.S. 828, 115 S.Ct. 97, 130 L.Ed.2d 47 (1994), where we held that “so long as the officer has probable cause to believe that a traffic violation has occurred or was occurring, the resulting stop is not unlawful and does not violate the Fourth Amendment.”
Mr. Ervin also argues that the length of the stop — approximately 45 minutes — unreasonably exceeded the time necessary to address the traffic violation. But a motorist may be detained after the purpose of a traffic stop is completed if “something that occur[s] during the stop cause[s] the officer to have a reasonable and articulable suspicion that criminal activity [i]s afoot.” United States v. Hill, 195 F.3d 258, 263 (6th Cir.1999), cert, denied, 528 U.S. 1176, 120 S.Ct. 1207, 145 L.Ed.2d 1110 (2000). In the case at bar Officer Haskell observed facts during the stop that gave him a “reasonable and articulable” suspicion of further criminal activity. Most significantly, Mr. Woodruff gave Haskell two false driver’s licenses before surrendering his own license. This suggested that Woodruff had reason to conceal his identity, and it justified investigation, at a minimum, into the validity of Woodruffs license. Haskell also noted that Woodruffs hands were extremely shaky and that Woodruff and Ervin gave inconsistent reasons for traveling to Miami. These facts contributed to Haskell’s reasonable suspicion of criminal activity. See id. at 271-72 (recognizing that inconsistent answers to questioning and nervous demeanor are factors that can contribute to reasonable suspicion).
Finally, Mr. Ervin claims that it was unreasonable for Officer Haskell to pat him down. Under the circumstances, we believe it was reasonable for the officer to conduct a protective pat-down search of Ervin for safety reasons. Any error in this regard would have been harmless, moreover, as the pat-down yielded only $2000 that was never connected to drug trafficking activity.
B
Mr. Ervin argues that the district court should have suppressed the evidence obtained in the search of the Kandy Kustoms body shop. He submits that the initial entry, made without a warrant, was illegal, while the affidavit supporting the search warrant was insufficient.
We shall assume, without so deciding, that the officers’ initial entry for the purpose of securing the body shop was not justified by exigent circumstances. But the fact that the entry, by hypothesis, was unjustified does not require suppression of the evidence found later during execution of the search warrant. The decision to obtain a search warrant was made before the initial entry, and the affidavit supporting the warrant did not rely on anything that was observed during the entry. In these circumstances, the challenged evi*636dence is clearly admissible under the “independent source” doctrine. See Segura v. United States, 468 U.S. 796, 814-15, 104 S.Ct. 3380, 82 L.Ed.2d 599 (1984), and Murray v. United States, 487 U.S. 533, 537, 108 S.Ct. 2529, 101 L.Ed.2d 472 (1988).
As to the sufficiency of Officer Dos-sett’s affidavit, we believe that the affidavit provided a substantial basis for concluding that there was probable cause to search Kandy Kustoms.2 The affidavit states that an informant, Robert Fears, obtained a kilogram of cocaine from Ervin at the Kandy Kustoms shop; that Fears saw more narcotics at the shop; and that Fears had previously purchased cocaine from Ervin both at the shop and elsewhere. The affidavit states further that Fears’ story was corroborated in part by independent information regarding sales of cocaine by Ervin. Under controlling Sixth Circuit case-law, this is sufficient to support a finding of probable cause. See United States v. Pelham, 801 F.2d 875, 878 (6th Cir.1986), cert. denied, 479 U.S. 1092, 107 S.Ct. 1305, 94 L.Ed.2d 160 (1987), where we approved an affidavit that named an informant and stated that the informant had personally observed the sale of drugs on the premises in the immediate past; see also United States v. Miller, 314 F.3d 265, 269-71 (6th Cir.2002), a case following Pelham.
Mr. Ervin argues that the affidavit contains a deliberately false statement — namely, that Ervin is the owner of Kandy Kustoms — and that therefore, under Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), he was entitled to a hearing on the affiant’s veracity. But Ervin has offered no evidence that the statement in question was deliberately, or even recklessly, false. Moreover, the statement was not necessary to the finding of probable cause. There was thus no call for a Franks hearing. See United States v. Hill, 142 F.3d 305, 310 (6th Cir.), cert. denied, 525 U.S. 898, 119 S.Ct. 225, 142 L.Ed.2d 185 (1998).
C
The district court’s refusal to suppress the evidence found in the search of the residence was also proper. Officer Dos-sett’s affidavit states that Mr. Fears saw drugs at Ervin’s residence within the previous 72 hours; that Fears purchased approximately 12 ounces of cocaine from Ervin “at that time;” and that Ervin had a “large amount” of cocaine remaining after the sale. The affidavit also states that Ervin was independently identified as a dealer of cocaine. Like the affidavit relating to Ervin’s place of business, this affidavit is sufficient to support a finding of probable cause. See Pelham, 801 F.2d at 878.
Mr. Ervin argues, as before, that the district court should have held a Franks hearing to determine whether the affidavit was tainted by deliberately false statements. The argument is based on Mr. Fears’ trial testimony that he actually purchased the 12 ounces of cocaine at a restaurant rather than at Ervin’s home. Again, however, Ervin has not shown that the affiant, Officer Dossett, knew of any falsity. And there is no evidence that Fears told Dossett that the sale of the 12 ounces — which was negotiated at the residence — was not consummated there as well.
Ill
Mr. Ervin argues that the district court abused its discretion by permitting *637federal agent Cordell Malone to give expert testimony on the mechanics of the drug trade. The crux of Ervin’s complaint is that many of the facts to which Agent Malone testified are common knowledge to people who watch police dramas on television. For that reason, Ervin says, Malone’s testimony was less an aid to the jury than a “second closing argument” for the government.
It is true that some of Agent Malone’s testimony — such as his statement that buyers and sellers of illegal drugs deal in cash — might have seemed self-evident to many jurors, if not necessarily to all. But much of Malone’s testimony would probably not have struck the jury as self-evident. It would not be obvious to everyone, for example, that drug dealers often transport drugs using vehicles rented in another person’s name; that a kilogram of cocaine sells for $20,000 to $30,000 in Chattanooga; or that crack cocaine is frequently sold in $20 “rocks.” And no substantial harm resulted, so far as we can tell, if Malone testified to some facts that the jury already knew. Any such testimony, in our view, did not amount to a “second closing argument.”
We have repeatedly upheld the admission of testimony similar to Agent Malone’s. See, e.g., United States v. Harris, 192 F.3d 580, 588-89 (6th Cir.1999); United States v. Thomas, 74 F.3d 676, 680-82 (6th Cir.), cert. denied, 517 U.S. 1162, 116 S.Ct. 1558, 134 L.Ed.2d 659 (1996); United States v. Pearce, 912 F.2d 159, 163 (6th Cir.1990), cert. denied, 498 U.S. 1093, 111 S.Ct. 978, 112 L.Ed.2d 1063 (1991). We see no reason to reach a different result here.
IV
Mr. Ervin’s next argument is that the district court abused its discretion by replacing the absent juror. The juror in question called in sick on the second day of deliberations and did not immediately return the court’s calls seeking to determine when she might be able to resume her service. The jury had deliberated only a short time on the previous day, and an alternate juror was available. In these circumstances, we cannot say that the district court abused its discretion. Mr. Ervin stresses that the dismissed juror was “the only minority juror.” However, the district court was not required on that basis to suspend the proceedings indefinitely while awaiting the juror’s return. Cf. Batson v. Kentucky, 476 U.S. 79, 85-86, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986) (acknowledging that “a defendant has no right to a petit jury composed in whole or in part of persons of his own race” (internal quotation marks omitted)).
V
Mr. Ervin raises several issues in connection with the determination of the quantity of drugs for which he was held responsible. He first contends that the district court should have instructed the jury to determine, beyond a reasonable doubt, the exact amount of drugs involved in his offenses. In this connection Mr. Ervin relies on Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), where the Supreme Court held that “[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt.” 530 U.S. at 490. But there is no Apprendi error here. The jury found, beyond a reasonable doubt, that Ervin was responsible for the threshold drug amounts charged in the indictment. Those amounts subjected Ervin to a statutory sentencing range of 10 years to life on counts I and II and five to 40 years on count III. See 21 U.S.C. §§ 846, 841(a)(1), 841(b)(1)(A), 841(b)(1)(B). The jury’s findings authorized the district court to impose any sen*638tence within that range — including the maximum, which is what the district court in fact imposed. Because Ervin did not receive a penalty that exceeded the statutory maximum, Apprendi did not require any additional jury findings. See Harris v. United States, 536 U.S. 545, 122 S.Ct. 2406, 2418, 153 L.Ed.2d 524 (2002) (“[T]he facts guiding judicial discretion below the statutory maximum need not be alleged in the indictment, submitted to the jury, or proved beyond a reasonable doubt”) (plurality opinion); United States v. Bums, 298 F.3d 523, 544 (6th Cir.) (“Apprendi is not triggered where the defendant receives a term of imprisonment within the statutory maximum ...” (internal quotation marks omitted)), cert. denied, — U.S. 123 S.Ct. 614, 642, 649, 154 L.Ed.2d 552 (2002).
At the very least, Mr. Ervin goes on to argue, the court should have applied a heightened standard — either “beyond a reasonable doubt” or “clear and convincing evidence.” That argument finds no support in Apprendi, see Harris, 122 S.Ct. at 2418, and is contrary to Sixth Circuit case-law requiring use of a “preponderance of the evidence” standard for proof of drug amounts at sentencing. See, e.g., United States v. Hough, 276 F.3d 884, 891 (6th Cir.), cert. denied, 535 U.S. 1089, 122 S.Ct. 1986,152 L.Ed.2d 1042 (2002).
Finally, Ervin argues that the district court erred in its calculation of the drug amounts. A district court’s determination of drug quantities may be based “on any competent evidence in the record” having a “minimum indicium of reliability,” and the court’s determination is reviewed only for clear error. Id.
Mr. Fears testified that he purchased from Mr. Ervin, or saw Ervin “cook,” at least three ounces of cocaine base on approximately 30 to 45 occasions. That testimony alone is sufficient to support the district court’s finding that 90 ounces of cocaine base could be attributed to Ervin. Ervin complains that Fears’ testimony was based on estimates of drug quantities and numbers of occurrences. In our view, however, the district court adequately accounted for that fact by using only the low ends of the ranges estimated by Fears. The district court’s calculation was not clearly erroneous.
As to the district court’s determination of the quantity of cocaine powder attributable to Mr. Ervin, the quantity determined by the court corresponded to the amounts that were actually recovered in the search of Kandy Kustoms, from Fears after his controlled purchase from Ervin, and from another drug customer who was apprehended after leaving Kandy Kustoms the night of the search. There was no clear error here either.
AFFIRMED.
. In connection with the latter point, Ervin urges us to adopt a rule that if a police officer has means to record the reasons for a stop, but does not avail himself of those means, the asserted reasons should be presumed to be false. We decline to create such a rule, but we note that an officer’s failure to obtain objective proof of a traffic violation when he might readily have done so may be considered in weighing the officer’s credibility.
. A court reviewing the sufficiency of a search warrant affidavit must determine, with "great deference” to the issuing judge, whether there was a "substantial basis” for issuance of the warrant. See, United States v. Allen, 211 F.3d 970, 972-73 (6th Cir.) (en banc), cert. denied, 531 U.S. 907, 121 S.Ct. 251, 148 L.Ed.2d 181 (2000).