Question

An exponential probability distribution has lambda equal to 21 customers per hour. Find the following probabilities....

An exponential probability distribution has lambda equal to 21 customers per hour. Find the following probabilities.

a) What is the probability that the next customer will arrive within the next 3 minutes​?

b) What is the probability that the next customer will arrive within the next 15 seconds?

c) What is the probability that the next customer will arrive within the next 12 minutes​?

d) What is the probability that the next customer will arrive within the next 17 minutes​?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Mean time of arrival = (60/21) minutes = 2.86 minutes

P(x) = 1 - e^(-x/2.86)

a) probability that the next customer will arrive within the next 3 minutes

1 - e^(-3/2.86) = 0.6496

b)

probability that the next customer will arrive within the next 15 seconds

1 - e^(-0.15/2.86) = 0.0511

c) probability that the next customer will arrive within the next 12 minutes​

1 - e^(-12/2.86) = 0.9849

d)   probability that the next customer will arrive within the next 17 minutes​

1 - e^(-17/2.86) = 0.9973

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