Customers make purchases at a convenience store, on average, every five and half

Question

Customers make purchases at a convenience store, on average, every five and half minutes. It is fair to assume that the time between customer purchases is exponentially distributed. Jack operates the cash register at this store. a-1. What is the rate parameter ? (Round your answer to 4 decimal places.) Rate parameter a-2. What is the standard deviation of this distribution? (Round your answer to 1 decimal place.) Standard deviation b. Jack wants to take a three-minute break. He believes that if he goes right after he has serviced a customer, he will lower the probability of someone showing up during his three-minute break. Is he right in this belief? Yes No c. What is the probability that a customer will show up in less than three minutes? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.) Probability d. What is the probability that nobody shows up for over fourty-five minutes? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.) Probability

Explanation / Answer

a-1)

rate parameter = 1/5.5 = 0.1818

a-2)

standard deviation of distribution = 5.5

b)

yes , as long as the service time is minimum

c)

P(T<3) = 1 -e^(-3/5.5)

= 0.4204

d)

P(T>45) = e^(-45/5.5)

= 0.0003

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