Question

A Costco employee performs a total of 60 movements of products within the store during a working
day. The duration of each movement follows an exponential distribution with mean 7 minutes, and the
movements are considered to be independent. What is the probability that the employee complete his
work before eight hours? If not specified, use a level of significance = 0:05

Answer 1

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P(X<8) = ?

Mean = 1/Lambda = ?

Lambda ( for 60 movements) in hours = (7minutes)*60 / 60 minutes = 7 hours

So, Mean = 1/7

x = 8, as we have to calculate  probability that the employee complete his work before eight hours

So, P(X<c) = 1- e^(-Lambda*c)

P(X<8) = 1- e^(-(1/7)*8) = .6811

So, probability that the employee complete his work before eight hours = 0.6811