Customers arrive at Rich Dunn’s Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich’s service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour. a) Find the average number of customers waiting for haircuts. b) Find the average number of customers in the shop. c) Find the average time a customer waits until it is his or her turn. d) Find the average time a customer spends in the shop. e) Find the percentage of time that Rich is busy.

a) 0.9,b) 1.5,c) 0.3hrs, d) 0.5hrs,e)  60%

Step-by-step explanation:

Given Data:

rate of arrival   = 3customers/hr ;

rate of service = 5 haircuts/hr    ;

a)

Average number of customers = La = λ²/[μ(μ-λ)]

                                                           = 3²/[(5(5-3)]

Average number of customers = La = 0.9

b)

Number of customers in system = Ls = λ/(μ-λ)

                                                             = 3/(5-3)

Number of customers in system = Ls = 1.5

c)

Average waiting time = Ta = λ/[μ(μ-λ)]

                                             = 3/[(5(5-3)]

Average waiting time = Ta =0.3hrs or 18mins

d)

Average time spent by customer = Ts = 1/(μ-λ)

                                                               = 1/(5-3)

Average time spent by customer = Ts = 0.5hrs or 30mins

e)

% of time  = Tr = λ/μ

                        = 3/5

% of time  = Tr = 0.6 or 60%

45

step-by-step explanation:

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: