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# Probability-Random Variable

Problem 1
The amount of time ships spend at the Philadelphia dockyard follows an exponential distribution and the average time spent in the dockyard is 3.1 days.
a. What is the probability that a randomly selected ship spends no more than 1.5 days at the dockyard?
b. What is the probability that a randomly selected ship spends more than 2 days at the dockyard?
Problem 2
The marketing division of Goodlife Tires determined the mean life of tires to be 30,000 miles with a standard deviation of 5,000 miles. Assume tire life is a normally distributed random variable.
a. What is the probability that tires last between 25,000 and 30,000 miles?
b. What is the probability that tires last between 28,000 and 33,000 miles?
c. What is the probability that tires last less than 28,000 miles?

Problem 3
The diameter of ½ inch bolts produced by a workshop is normally distributed with a mean of 0.5 inch and a standard deviation of 0.04 inch. What is the probability that a bolt selected at random will fit in a hole whose diameter is between 0.475 inch and 0.525 inch?

#### Solution Summary

The solution contains the determination of different kinds of probabilities when the random variable under consideration follows exponential and normal distributions.

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