OPINION
WILLIAMS, Circuit Judge:
Walter Lee Chambers and James Isaac Johnson appeal their jury convictions and sentences for: (1) conspiracy to possess with intent to distribute in excess of five kilograms of cocaine, 21 U.S.C. § 846 (1988); (2) conducting an illegal gambling business, 18 U.S.C. § 1955 (1988); and (3) conspiracy to commit an offense against the United States (i.e., to conduct an illegal gambling business), 18 U.S.C. § 371 (1988). Chambers contends that the district court erred in concluding that he was a manager or supervisor and increasing his offense level under § 3Bl.l(b) of the Sentencing Guidelines. United States Sentencing Commission, Guidelines Manual (Nov. 1991). Chambers urges the evidence did not support finding that he was a manager or supervisor because it did not show that he supervised any people. Chambers also contends that the district court clearly erred in finding that the drug conspiracy involved at least fifteen kilograms of cocaine. In addition, both Defendants challenge the sufficiency of evidence supporting their convictions and the failure of the district court to admit as exculpatory evidence the results of a witness’s polygraph examination.
Although we conclude the evidence did not show that Chambers supervised people, we also conclude that supervision of people is not necessary to be a manager under § 3Bl.l(b). Because the district court did not make any factual findings based upon Chambers’s role as a manager, we vacate Chambers’s sentence and remand for further fact-finding and resentencing. In all other respects, we affirm the judgments of the district court.
I
Chambers and Johnson were among twenty-three persons indicted for conducting and conspiring to conduct an illegal gambling business and were among fifteen persons indicted for conspiracy to distribute cocaine.
The cocaine conspiracy involved five cocaine houses including the “Big House,” the “Yellow House,” the “Blue Light,” and “Cozy’s.” The evidence presented at trial focused primarily on Cozy’s. Cozy’s was the quintessential drug house. Steel bars shielded the doors and windows. Upon entering Cozy’s a buyer came upon a second door with a mail slot that shielded a separate interior room. Behind the mail slot in this separate room, a coconspirator would “work the trap,” i.e., exchange the buyer’s cash for cocaine. The second door and interior room created a barrier for law enforcement officers to penetrate before they could actually seize the cocaine. Each morning a coconspirator would light a fire in the fireplace to destroy cocaine in case of a police search, regardless of the season or the temperature outside.
The gambling conspiracy involved an illegal numbers lottery. Bets were accepted at various locations. “Runners” or “bag-men” would take the bettors’ tickets to a drop off point. The tickets were then transferred to a “bank” or “tally house” where the winning bets were determined. The location of the bank was frequently changed to avoid detection. After the win[1266]*1266ning tickets had been identified, the tickets would be put in storage for three or four days in case a winning ticket had been overlooked.
Following indictment, most of the cocon-spirators pled guilty pursuant to plea agreements. Chambers and Johnson chose to go to trial, and the testimony of their numerous coconspirators featured prominently in the case against them. The jury convicted them on all counts. Chambers was sentenced to 210 months imprisonment based upon a total offense level of 37. The sentence included a three level upward adjustment pursuant to § 3Bl.l(b) of the Sentencing Guidelines for being a manager or supervisor. Johnson was sentenced to 121 months imprisonment based upon a total offense level of 32. Both Defendants appealed.
II
Chambers contends that the district court erred in finding that he was a manager or supervisor and increasing his offense level under § 3Bl.l(b) of the Sentencing Guidelines.1 He urges that the evidence does not support a finding that he supervised people, and therefore does not support a § 3Bl.l(b) adjustment. We agree that the evidence does not support finding supervision of people; however, we conclude that under some circumstances a defendant's offense level may be increased under § 3Bl.l(b) even though the defendant did not supervise anyone. Nevertheless, because the district court’s factual findings were insufficient, we remand for further fact-finding and resentencing.
A
Section 3B1.1 “provides a range of adjustments to increase [a defendant’s] offense level based upon the size of a criminal organization ... and the degree to which the defendant was responsible for committing the offense.” U.S.S.G. § 3B1.1, comment, (backg’d). Application of the guideline involves two separate factual inquiries. First, the district court must determine the size or scope of the criminal organization. If the criminal activity involved five or more participants “or was otherwise extensive,” then either § 3Bl.l(a) or (b) may apply. Otherwise, § 3Bl.l(c) may apply. Second, the district court must evaluate the defendant’s role in the offense. If the defendant was an organizer, leader, manager, or supervisor, then the defendant’s offense level should be increased. With smaller criminal organizations, the increase in the defendant’s offense level is the same for each of these four roles. Id. § 3Bl.l(c) (two level increase). With larger organizations (i.e., those with five or more participants), the offense level is increased more for organizers and leaders, id. § 3Bl.l(a) (four level increase), than for managers and supervisors, id. § 3Bl.l(b) (three level increase).
Chambers does not dispute the district court’s determination that the conspiracy involved five or more participants, nor does the Government contend that he was an organizer or leader. The dispute is over whether he was a manager or supervisor.
Although the Government asked the district court to increase Chambers’s base offense level based on his role as a manager, the district court’s only factual finding was that Chambers “was a supervisor at some level.” The district court thus treated terms “manager” and “supervisor” as synonymous. We shall treat the district court’s finding as one that Chambers was a manager, as argued by the Government at sentencing, and therefore we do not ad[1267]*1267dress whether there is a distinction between the two terms as used in § 3B1.1.
B
We agree with Chambers that the evidence does not support a finding that he supervised people. Chambers’s coconspirators testified at trial about his role in the conspiracy. They were consistent in their portrayal of what he did. They testified that Chambers was one of three or four individuals who would bring cocaine to Cozy’s when the house ran low on stock, pick up the cash on hand, and take the cash away. In addition, James Edward “Ned” Johnson, the “kingpin” of the cocaine conspiracy, testified that he and Chambers were responsible for going to the stash-house, packaging the cocaine for resale, and transferring the packaged cocaine to Cozy’s.
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OPINION
WILLIAMS, Circuit Judge:
Walter Lee Chambers and James Isaac Johnson appeal their jury convictions and sentences for: (1) conspiracy to possess with intent to distribute in excess of five kilograms of cocaine, 21 U.S.C. § 846 (1988); (2) conducting an illegal gambling business, 18 U.S.C. § 1955 (1988); and (3) conspiracy to commit an offense against the United States (i.e., to conduct an illegal gambling business), 18 U.S.C. § 371 (1988). Chambers contends that the district court erred in concluding that he was a manager or supervisor and increasing his offense level under § 3Bl.l(b) of the Sentencing Guidelines. United States Sentencing Commission, Guidelines Manual (Nov. 1991). Chambers urges the evidence did not support finding that he was a manager or supervisor because it did not show that he supervised any people. Chambers also contends that the district court clearly erred in finding that the drug conspiracy involved at least fifteen kilograms of cocaine. In addition, both Defendants challenge the sufficiency of evidence supporting their convictions and the failure of the district court to admit as exculpatory evidence the results of a witness’s polygraph examination.
Although we conclude the evidence did not show that Chambers supervised people, we also conclude that supervision of people is not necessary to be a manager under § 3Bl.l(b). Because the district court did not make any factual findings based upon Chambers’s role as a manager, we vacate Chambers’s sentence and remand for further fact-finding and resentencing. In all other respects, we affirm the judgments of the district court.
I
Chambers and Johnson were among twenty-three persons indicted for conducting and conspiring to conduct an illegal gambling business and were among fifteen persons indicted for conspiracy to distribute cocaine.
The cocaine conspiracy involved five cocaine houses including the “Big House,” the “Yellow House,” the “Blue Light,” and “Cozy’s.” The evidence presented at trial focused primarily on Cozy’s. Cozy’s was the quintessential drug house. Steel bars shielded the doors and windows. Upon entering Cozy’s a buyer came upon a second door with a mail slot that shielded a separate interior room. Behind the mail slot in this separate room, a coconspirator would “work the trap,” i.e., exchange the buyer’s cash for cocaine. The second door and interior room created a barrier for law enforcement officers to penetrate before they could actually seize the cocaine. Each morning a coconspirator would light a fire in the fireplace to destroy cocaine in case of a police search, regardless of the season or the temperature outside.
The gambling conspiracy involved an illegal numbers lottery. Bets were accepted at various locations. “Runners” or “bag-men” would take the bettors’ tickets to a drop off point. The tickets were then transferred to a “bank” or “tally house” where the winning bets were determined. The location of the bank was frequently changed to avoid detection. After the win[1266]*1266ning tickets had been identified, the tickets would be put in storage for three or four days in case a winning ticket had been overlooked.
Following indictment, most of the cocon-spirators pled guilty pursuant to plea agreements. Chambers and Johnson chose to go to trial, and the testimony of their numerous coconspirators featured prominently in the case against them. The jury convicted them on all counts. Chambers was sentenced to 210 months imprisonment based upon a total offense level of 37. The sentence included a three level upward adjustment pursuant to § 3Bl.l(b) of the Sentencing Guidelines for being a manager or supervisor. Johnson was sentenced to 121 months imprisonment based upon a total offense level of 32. Both Defendants appealed.
II
Chambers contends that the district court erred in finding that he was a manager or supervisor and increasing his offense level under § 3Bl.l(b) of the Sentencing Guidelines.1 He urges that the evidence does not support a finding that he supervised people, and therefore does not support a § 3Bl.l(b) adjustment. We agree that the evidence does not support finding supervision of people; however, we conclude that under some circumstances a defendant's offense level may be increased under § 3Bl.l(b) even though the defendant did not supervise anyone. Nevertheless, because the district court’s factual findings were insufficient, we remand for further fact-finding and resentencing.
A
Section 3B1.1 “provides a range of adjustments to increase [a defendant’s] offense level based upon the size of a criminal organization ... and the degree to which the defendant was responsible for committing the offense.” U.S.S.G. § 3B1.1, comment, (backg’d). Application of the guideline involves two separate factual inquiries. First, the district court must determine the size or scope of the criminal organization. If the criminal activity involved five or more participants “or was otherwise extensive,” then either § 3Bl.l(a) or (b) may apply. Otherwise, § 3Bl.l(c) may apply. Second, the district court must evaluate the defendant’s role in the offense. If the defendant was an organizer, leader, manager, or supervisor, then the defendant’s offense level should be increased. With smaller criminal organizations, the increase in the defendant’s offense level is the same for each of these four roles. Id. § 3Bl.l(c) (two level increase). With larger organizations (i.e., those with five or more participants), the offense level is increased more for organizers and leaders, id. § 3Bl.l(a) (four level increase), than for managers and supervisors, id. § 3Bl.l(b) (three level increase).
Chambers does not dispute the district court’s determination that the conspiracy involved five or more participants, nor does the Government contend that he was an organizer or leader. The dispute is over whether he was a manager or supervisor.
Although the Government asked the district court to increase Chambers’s base offense level based on his role as a manager, the district court’s only factual finding was that Chambers “was a supervisor at some level.” The district court thus treated terms “manager” and “supervisor” as synonymous. We shall treat the district court’s finding as one that Chambers was a manager, as argued by the Government at sentencing, and therefore we do not ad[1267]*1267dress whether there is a distinction between the two terms as used in § 3B1.1.
B
We agree with Chambers that the evidence does not support a finding that he supervised people. Chambers’s coconspirators testified at trial about his role in the conspiracy. They were consistent in their portrayal of what he did. They testified that Chambers was one of three or four individuals who would bring cocaine to Cozy’s when the house ran low on stock, pick up the cash on hand, and take the cash away. In addition, James Edward “Ned” Johnson, the “kingpin” of the cocaine conspiracy, testified that he and Chambers were responsible for going to the stash-house, packaging the cocaine for resale, and transferring the packaged cocaine to Cozy’s. Only Chambers, Ned Johnson, and Pee Wee Givens knew the location of the stashhouse.2
Although the witnesses testified that Ned Johnson hired and paid them, no one testified that Chambers performed a single supervisory task. Indeed, of the ten witnesses involved in the cocaine conspiracy, none testified that Chambers supervised anyone. Moreover, the basis for a § 3Bl.l(b) adjustment given in the presen-tence report was Chambers’s “high ranking position within the conspiracy” and his privileged knowledge of the location of the stashhouse. (J.A. 741.) The presentence report does not indicate that Chambers supervised any of his coconspirators. In short, the evidence does not support finding that Chambers supervised people.
C
Chambers argues that a defendant who did not supervise people cannot be considered a manager or supervisor within the meaning of § 3Bl.l(b). We disagree. In United States v. Paz, 927 F.2d 176 (4th Cir.1991), we affirmed a defendant’s sentence based upon his management of property. In Paz, the defendant argued that the evidence showed he was a courier, not a manager. We disagreed:
[EJvidence indicated that Paz controlled the money, drug products and residences where the drug trafficking was performed. From this evidence, the district court concluded that Paz was a manager of the enterprise. We are not persuaded that this factual determination was clearly erroneous.
Id. at 180; see also United States v. Johnson, 906 F.2d 1285, 1291-92 (8th Cir.1990) (“A finding that a defendant is functioning as an organizer or leader, however, does not necessarily mean that he is directly controlling other individuals.”); United States v. Mares-Molina, 913 F.2d 770, 776 (9th Cir.1990) (Rymer, J., dissenting) (plain meaning of “manager” includes management of property).
Other circuits have disagreed with our holding in Paz. See United States v. Fuentes, 954 F.2d 151, 154 (3d Cir.), cert. denied, — U.S. -, 112 S.Ct. 2950, 119 L.Ed.2d 573 (1992); United States v. Mares-Molina, 913 F.2d 770, 773-74 (9th Cir.1990); United States v. Reid, 911 F.2d 1456, 1464 (10th Cir.1990), cert. denied, — U.S. -, 111 S.Ct. 990, 112 L.Ed.2d 1074 (1991); United States v. Fuller, 897 F.2d 1217, 1220-21 (1st Cir.1990). They make two arguments in favor of requiring supervision of people: (1) the term “manager” implicitly requires supervision of people; and (2) management of property is an insufficient basis for determining relative culpability. We respectfully disagree with both conclusions.
To determine the meaning of the term “manager” we apply principles of statutory construction. Statutory interpretation begins with the language of the statute itself. Ardestani v. I.N.S., — U.S. -, -, 112 S.Ct. 515, 519, 116 L.Ed.2d 496 (1991). Except in “rare and exceptional circumstances,” statutory language is given its plain meaning as expressed by the ordinary meaning of the words used. Id. at -, 112 S.Ct. at 520.
[1268]*1268The Guidelines do not define the term “manager.” Application note 3 to § 3B1.1 does provide a list of factors to be considered in distinguishing between the roles of leader, organizer, manager, and supervisor. Although the “degree of control and authority exercised over others” is one factor, the application note pointedly does not make this factor a requirement for any of these roles. If a requirement for supervision of people can be found, it must derive from the term “manager” itself. Because the Guidelines do not define the term “manager,” we turn to its dictionary definition.
Webster’s defines “manager” as “a person whose work or profession is the management of a specified thing (as a business, an institution, or a particular phase or activity within a business or institution).” Webster’s Third New International Dictionary 1372 (1986) (emphasis added). In a similar vein, Random House defines “manager” as “a person who has control or direction of an institution, business, etc., or of a part, division or phase of it,” The Random House Dictionary of the English Language 1166-67 (2d ed.1987), and Oxford defines “manager” as “[o]ne whose office it is to manage a business establishment or a public institution.” 6 The Oxford English Dictionary 106 (1933). Supervision of people is required by none of these definitions. Whether management requires supervision of people depends upon what is being managed. A manager of a department within a labor-intensive business supervises people; a manager of a small apartment building or of investments does not. Accordingly, construing the term “manager” in accord with its plain meaning, we hold that one who manages property without supervising people can be a “manager” within the meaning of § 3Bl.l(b).
Properly applied, this interpretation is consistent with the primary goal of § 3B1.1, namely, the determination of a defendant’s culpability relative to other participants in a criminal activity “based upon the role the defendant played in committing the offense.” U.S.S.G. ch. 3, pt. B, intro, comment. We are mindful of the concern that management of property may not be as sound a basis for determining relative culpability as supervision of people. As one court has noted, “[t]he lowliest participant in a criminal enterprise can ordinarily be said to manage, in the broad sense of that word, some segment or property of the enterprise.” Fuentes, 954 F.2d at 153-54.
This concern does not, however, require a narrow construction of the term “manager.” Rather, the solution lies in focusing on the factors identified in the Sentencing Guidelines for distinguishing between leaders, organizers, managers, supervisors, and other participants in a criminal activity. These factors include:
the exercise of decision making authority, the nature of participation in the commission of the offense, the recruitment of accomplices, the claimed right to a larger share of the fruits of the crime, the degree of participation in planning or organizing the offense, the nature and scope of the illegal activity, and the degree of control and authority exercised over others.
U.S.S.G. § 3B1.1, comment, (n.3). Of these seven factors, only one, the “degree of control and authority exercised over others,” relates to supervision of people.
Under these factors, neither mere possession of property nor mere service as a courier supports increasing a defendant’s offense level as a manager. In at least some cases, however, application of these factors to the evidence may show that, although a defendant did not supervise people, his extensive management responsibilities over property, assets, or activities of the criminal organization justifies increasing his offense level pursuant to § 3Bl.l(b). For example, the person masterminding the money laundering component of a large drug conspiracy may exercise considerable decision making authority, may lay claim to a large share in the proceeds of the crime, and may be a central participant in the criminal activity without ever supervising anybody. His role may be less significant than that of the leader or organizer, but of equivalent culpability [1269]*1269with that of the supervisor of a drug house staff. Thus, an increase in offense level under § 3Bl.l(b) based on a defendant’s role as a manager is justified where application of these factors indicates that the defendant’s role in the offense was greater than that of less responsible participants.
D
The district court’s factual findings supporting the upward adjustment in Chambers’s sentence were limited to a statement that Chambers “was at least a supervisor at some level.” We find no basis in the record for concluding that the district court considered the factors outlined in application note 3 in making this finding. The evidence may or may not support the conclusion that Chambers was a manager or supervisor. However, without specific factual findings showing that the district court evaluated the defendant’s role in the offense in light of the factors in application note 3, we cannot conduct meaningful appellate review of this issue. Accordingly, we vacate Chambers’s sentence and remand.3
On remand, the district court should apply the factors outlined in application note 3 and determine whether Chambers’s role in the conspiracy was sufficiently extensive to warrant an increase in offense level under § 3Bl.l(b). See United States v. Brooks, 957 F.2d 1138, 1150 (4th Cir.) (adjustment not supported by evidence relied on by district court, but other evidence could support it on remand), cert. denied, — U.S. -, 112 S.Ct. 3051, 120 L.Ed.2d 917 (1992). If an increase is warranted, then the district court should identify which factors in application note 3 justify its decision.
Ill
Chambers also challenges the district court’s finding that the conspiracy involved at least fifteen kilograms of cocaine. We review this finding for clear error. 18 U.S.C. § 3742(e).
The evidence showing how much cocaine was distributed consisted of estimates by various witnesses of the amount of cash taken in during a shift at Cozy’s. Sylvester Springs, for example, testified that during 1987 the average weekly intake of cash was around $40,000 to $45,000. He further testified that from the middle of 1988 through 1989 the average weekly intake was around $60,000. Ned Johnson testified that Cozy’s operated for around two and one-half years, ending its operations in early 1990. Police testimony indicated that the street price of a kilogram of cocaine was $200,000. At this price, 200 grams of cocaine per week were distributed in 1987 and in the first half of 1988 and 300 grams of cocaine per week were distributed in the second half of 1988 and in 1989. This amounts to 5.2 kilograms of cocaine in the last half of 1987, 13.0 kilograms in 1988, and 15.6 kilograms in 1989. Other witnesses gave varying estimates of the amount of cash taken in on a given shift, most of which exceeded those given by Springs. Three witnesses, for example, testified that the least amount of money they had seen on a shift was $4,000, whereas Springs testified that he had seen as little as $1,000. Springs’s figures thus appear to be conservative compared to those of other witnesses. Because these witnesses’ testimony readily supports finding that over fifteen kilograms of cocaine was distributed at Cozy’s during the course of the conspiracy, the district court did not clearly err in attributing fifteen kilograms to the conspiracy for purposes of sentencing.
IV
Both Defendants challenge the sufficiency of evidence to support their convictions.
We review the sufficiency of the evidence under the familiar standard of Jackson v. Virginia, 443 U.S. 307, 319, [1270]*127099 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979), which inquires whether “any rational trier of fact could have found the essential elements of the crime [charged] beyond a reasonable doubt,” and requires us in applying the standard to construe the evidence in the light most favorable to the government, assuming its credibility, drawing all favorable inferences from it, and taking into account all the evidence, however adduced.
United States v. Giunta, 925 F.2d 758, 764 (4th Cir.1991).
Defendants were each convicted of two counts involving conspiracies. In a conspiracy case, the Government must show that: (1) a conspiracy existed; (2) the Defendants had knowledge of the conspiracy; and (3) the Defendants voluntarily became part of the conspiracy. United States v. Bell, 954 F.2d 232, 236 (4th Cir.1992). “[T]he existence of a conspiratorial agreement need not be proven by direct evidence, but may be inferred from the facts and circumstances of the case, i.e., circumstances indicating that two or more people acted in concert to achieve an illegal goal.” United States v. Laughman, 618 F.2d 1067, 1074 (4th Cir.1980), cert. denied, 447 U.S. 925, 100 S.Ct. 3018, 65 L.Ed.2d 1117 (1980).
Ned Johnson’s testimony is sufficient to support Defendants’ convictions for conspiracy to distribute cocaine. Ned Johnson testified that he hired Defendant James Isaac Johnson to work at the front door of Cozy’s where he identified customers before allowing them entrance into the drug house. He eventually became a shift manager. Ned Johnson also testified that Defendant Chambers’s principal job was to go to the stashhouse where the cocaine was stored, break down the cocaine, package it in sandwich bags, and transport the bags to Cozy’s. From this evidence the jury could have inferred an agreement to distribute cocaine, knowledge of the agreement, and voluntary participation in the conspiracy.
The strongest evidence supporting Defendants’ convictions for conspiracy to conduct an illegal gambling business was the testimony of Gloria Jean Holloway, the bookkeeper of the gambling operation. She testified that the Defendants brought tickets to the bank where the winning tickets were determined. After Holloway determined which tickets were winners, the Defendants would take the tickets to a storage place. Ned Johnson, who also headed the gambling conspiracy, testified that both Defendants knew that they were transporting lottery tickets because the Defendants were occasionally asked to look in the envelopes and see whether any of the tickets had a winning number. This evidence indicates that the Defendants acted in concert with Holloway, Ned Johnson, and other conspirators to conduct an illegal gambling operation. Circumstances indicating that parties acted in concert to achieve a criminal goal are sufficient to support the inference of an agreement or conspiracy. Bell, 954 F.2d at 236. Ned Johnson’s testimony that the Defendants knew the envelopes contained lottery tickets supported finding that the Defendants knew of the conspiracy and voluntarily participated in it. The Government therefore produced sufficient evidence to support the convictions for conspiracy to conduct an illegal gambling operation. Holloway’s testimony also established that the conspirators conducted a gambling operation that was illegal under North Carolina law; thus, the evidence supported Defendants’ conviction on that count as well.
V
At trial, Defendants sought to impeach the testimony of Gloria Jean Holloway by introducing the results of a polygraph examination she had failed to pass. Defendants urge that the district court erred in excluding all evidence of the results of the polygraph examination. We disagree. In United States v. A & S Council Oil Co., 947 F.2d 1128, 1134 (4th Cir.1991), we held that the results of a polygraph examination were not admissible to impeach the credibility of a witness. We explicitly rejected the argument that the results of a polygraph examination are admissible as exculpatory as opposed to incul-[1271]*1271patory evidence. The district court, therefore, did not err in excluding the polygraph evidence.
VI
For the foregoing reasons, we affirm Johnson’s conviction and sentence. We affirm Chambers’s conviction, vacate his sentence, and remand for resentencing.
No. 91-5190: AFFIRMED IN PART, VACATED IN PART, AND REMANDED.
No. 91-5191: AFFIRMED.