# Find the probability that if three professors are randomly selected, all three work for more than 60 hours per week.The amount of time the university professors devote to their jobs per week is...

Find the probability that if three professors are randomly selected, all three work for more than 60 hours per week.

The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 and a standard deviation of 6 hours.

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### 2 Answers

The time per week for which university professors work is 52 hours with a standard deviation of 6 hours.

If three professors are randomly selected the probability that all three work for more than 60 hours has to be determined.

The z-score for the number of hours spent working being equal to 60 is (60 - 52)/6 = 1.33

The probability of the number of hours worked for being less than 60 that is obtained from a normal table using this z-score is 0.9082. The probability that the professors work more than 60 hours is 1 - 0.9082 = 0.0918

**There is a 9.18% probability that the professors chosen at random work for more than 60 hours.**

a)What is the probability that a professor works for more than 60 hours per week?

P(X>60) = P(Z>1.33) = 1 - P(Z<1.33) = 1 - .9082 = .0918,

using Zscore (60): (60-52)/6 = 1.33

b)Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours.

μx=52, σ=6/(3^1/2)=3.46

P(X>60) = P(Z<2.31) = 1-P(Z<2.31) = 1-.9896=.0104