Question

Customers make purchases at a convenience store, on average, every nine 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 λ? (Round your answer to 4 decimal places.)


a-2. What is the standard deviation of this distribution? (Round your answer to 1 decimal place.)


b. Jack wants to take a seven-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 seven-minute break. Is he right in this belief?

• Yes

• No

c. What is the probability that a customer will show up in less than seven minutes? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

d. What is the probability that nobody shows up for over half an hour? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Answer 1

a-1)

λ =1/9 =

0.1111

a-2)

standard deviation σ=

1/λ=β =

9.00

b)

No

c)

P(X<7)=1-exp(-7/9)=

0.5406

d)

P(X>30)=1-P(X<30)=1-(1-exp(-30/9))=

0.0357