Question

In: Statistics and Probability

Suppose that the service time at a store with only, one check-out counter is Exponentially distributed,...

Suppose that the service time at a store with only, one check-out counter is Exponentially distributed, with a mean time of 10 minutes.

a) What is the probability that a customer who is first in line now will spend more than 15 minutes waiting in the check-out line? (Solve using Exponential distribution and then using Poisson.)

b) A customer has already been waiting in the line for more than 10 minutes. What is the probability that this customer will still be at the store in more than 15 minutes from now?

c) What is the probability of spending less than a half an hour at the check-out? (Solve using two different time units.)

Solutions

Expert Solution

It is given that the service time at a store with only, one check-out counter is Exponentially distributed, with a mean time of 10 minutes. The PDF is .

a) The required probability is

The Poisson equivalent is no one person arrive in the first 15 minutes. Here .

The number of persons in 15 minutes has distribution .

The required probability is

b) The required conditional probability is

c)  The required probability is

orchestra answered 1 year ago
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