Question

Customers make purchases at a convenience store, on average, every sixteen 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.) Rate parameter λ ______________

a-2. What is the standard deviation of this distribution? Standard deviation _____________________

b. Jack wants to take a 12-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 12-minute break. Is he right in this belief? Yes or No

c. What is the probability that a customer will show up in less than 12 minutes? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability __________

d. What is the probability that nobody shows up for over 20 minutes? (Round your intermediate calculations and final answer to 4 decimal places.)

Answer 1

Solution :

a-1)

rate parameter = 1/16= 0.0625

a-2)

standard deviation of distribution = 0.0625

b)

No, he is not belief in because the probabilities are memoryless

c)

P(T<12) = 1 -e^(-12/16)

= 0.5276

d)

P(T>20) = e^(-20/16)

= 0.2865.

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