We are given that the average number of hours worked is 52 hours with a standard deviation of 6 hours. We are asked to find the probability that three randomly selected professors each work more than 60 hours.

(1) First we find the probability that a randomly chosen person works...

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We are given that the average number of hours worked is 52 hours with a standard deviation of 6 hours. We are asked to find the probability that three randomly selected professors each work more than 60 hours.

(1) First we find the probability that a randomly chosen person works more than 60 hours.

Assuming that the hours are normally distributed, we can convert to a standard normal score:

`z=(X-mu)/sigma=(60-52)/6=1.bar(3)`

Now we can use the standard normal table (or some utility) to find the probability that a randomly chosen person exceeds 60 hours:

`P(X>60)=P(z>1.33)~~.0918` (Using the rounded value of 1.33; using the exact value yields .0912)

(2) Now we assume that the hours each professor works is independent, so the probability of three such professors working more than 60 hours is `.0918^3~~.00077`

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