Suppose that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 180 seconds.

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Question

Suppose that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 180 seconds.

Suppose that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 180 seconds. a. What is the probability that the time between the arrivals of two customers will be less than 108 seconds? b. What is the probability that the time between the arrivals of two customers will be between 44 and 134 seconds? c. What is the probability that the time between the arrivals of two customers will be greater than 124 seconds? d. What are the mean and standard deviation of the time between the arrival of two customers?

math Statistics-And-Probability

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Answer 1

Answer #1

Solution:

We know that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 180 seconds.

Therefore, we have:

a. What is the probability that the time between the arrivals of two customers will be less than 108 seconds?

Answer: We have to find

Using the uniform distribution model, we have:

Therefore, the probability that the time between the arrivals of two customers will be less than 108 seconds is

b. What is the probability that the time between the arrivals of two customers will be between 44 and 134 seconds?

Answer: We have to find

Using the uniform distribution model, we have:

Therefore, the probability that the time between the arrivals of two customers will be between 44 and 134 seconds is

c. What is the probability that the time between the arrivals of two customers will be greater than 124 seconds?

Answer: We have to find

Using the uniform distribution model, we have:

Therefore, the probability that the time between the arrivals of two customers will be greater than 124 seconds is

d. What are the mean and standard deviation of the time between the arrival of two customers?

Answer:

The mean is given below:

The standard deviation is given below:

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Answer 2

Suppose that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 180 seconds.

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Suppose that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 180 seconds.

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