A hair salon provides low-cost haircuts at a shopping center in Boise, Idaho. During the day, customers arrive at an average rate of 8 per hour following a Poisson distribution. After a customer is in a cosmetician's chair, it takes an average of 21 minutes for the haircut to be completed, with the actual service time following an exponential distribution. (Round your answers to four decimal places.) (a) If there are 3 cosmetician's on duty, how many customers are typically waiting for service?  ______ customers How long will customers have to wait on average (in minutes) before receiving service?  ______ minutes (b) If there are 4 cosmetician's on duty, how many customers are typically waiting for service?  ______ customers How long will customers have to wait on average (in minutes) before receiving service?  ______ minutes (c) If there are 5 cosmetician's on duty, how many customers are typically waiting for service?  ______ customers How long will customers have to wait on average (in minutes) before receiving service?  ______ minutes (d) If you managed this store, how many cosmetician's would you employ and why?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
Question
A hair salon provides low-cost haircuts at a shopping center in Boise, Idaho. During the day, customers arrive at an average rate of 8 per hour following a Poisson distribution. After a customer is in a cosmetician's chair, it takes an average of 21 minutes for the haircut to be completed, with the actual service time following an exponential distribution. (Round your answers to four decimal places.)
(a) If there are 3 cosmetician's on duty, how many customers are typically waiting for service?
 ______ customers
How long will customers have to wait on average (in minutes) before receiving service?
 ______ minutes

(b) If there are 4 cosmetician's on duty, how many customers are typically waiting for service?
 ______ customers
How long will customers have to wait on average (in minutes) before receiving service?
 ______ minutes

(c) If there are 5 cosmetician's on duty, how many customers are typically waiting for service?
 ______ customers
How long will customers have to wait on average (in minutes) before receiving service?
 ______ minutes

(d) If you managed this store, how many cosmetician's would you employ and why?
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