Assume the time required to pass through security at a particular airport follows the continuous uniform distribution

Question:

Assume the time required to pass through security at a particular airport follows the continuous uniform distribution with a minimum time of 5 minutes and maximum time of 30 minutes.

a. Calculate the value of f(x).

b. What are the mean and standard deviation for this distribution?

c. What is the probability that the next passenger will require less than 25 minutes to pass through security?

d. What is the probability that the next passenger will require more than 20 minutes to pass through security?

e. What is the probability that the next passenger will require between 8 and 15 minutes to pass through security?

f. What time represents the 75th percentile of this distribution?

Distribution
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