Question

Customers make purchases at a convenience store, on average, every ten 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 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 nine-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 nine-minute break. Is he right in this belief?

• Yes

• No

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

Answer 1

ANSWER:-

     Rate parameter λ :

The standard deviation of this distribution : eleven and half minute.

  The probability that a customer will show up in less than seven minutes :

Since times between purchases are exponentially distributed with average of eleven and half minute , the distribution is given by
P( T < t) = 1 - e^(-t/11.5), and you want t = 7, so, P(T < 7) = 1 - e^(7/11.5)

Probability that nobody shows up for over forty-five minutes :

  P( T > 45) = e^(-45/6) = 1808.0424