1Waiting times to receive food after placing an order at the

1.Waiting times to receive food after placing an order at the local sandwich shop follow an exponential distribution with a mean of 60 seconds. Calculate the probability a customer waits:

a.Less than 30 seconds.

b.More than 120 seconds.

c.Between 45 and 75 seconds.

Solution

As mean = 60, then the cumulative distribution is

P(X<=x) = F(x) = 1 - exp(-(1/60)*x)

Thus,

a)

P(x<30) = F(30) = 1 - exp(-(1/60)*30) = 0.39346934 [ANSWER]

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b)

P(x>120) = 1 - F(120) = exp(-(1/60)*120) = 0.135335283 [ANSWER]

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c)

P(45<x<75) = F(75) - F(45) = exp(-(1/60)*45) - exp(-(1/60)*75) = 0.185861756 [ANSWER]