1) Suppose that X is a normal random variable with a mean of 10 and a variance of 16. What is the standardized value for x=8? That is, what is the value for z such that P[X<=8] = P[Z<=z].
2) The time between calls to a busy department is exponentially distributed with a mean of 5 minutes. What is the probability that there are no calls within a twenty minute interval?
3) Suppose you run a used tire store, and you know half of the tires you have in stock are good and half are bad. You need four good tires to finish servicing a car. If you send your assistant into the warehouse to get six tires, you wonder if you will have enough good tires to finish the job. What distribution best fits this situation and what are the parameters for that distribution? You do not need to solve the problem.
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