Question

Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 2.0 minutes and standard deviation of 4.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n = 31 customers in the first line and n2 = 42 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X, and the mean service time for the longer one X is more than 0.2 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P= the absolute tolerance is +/-0.01

Answer 1

Solation The Li Sonvice me th a mean MIM Omin ond standand deviation Sonvice Countou have the same distoibutio 4.0 clde to a nlmal distofbuton and mim Let D +the diffesence Sm Sample mean Oice imes beuen the aing th ne zu h, 31 and n242 D has a nalmal disto bertion oth the mean Ma M22.0- 2.0 - 0 and a stan dard deriati on aiven by 42 42 2 2 - 0.9471 42 + we coant to Pind the pooboby that the dference butween 31 the shoter Bne ime P Sence the mean and the mon sove me fo tha lages s male than one 0.2 minutor D0.2 PCD0.2) oe) 17 0.9471 = 1 - 0.5832 0.4168 Cuing the 14 Stondaod nBlmal tade) yous a Sbc

P value = 0.42