Question

Q.1) The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours.

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

b) Find the probability that the mean amount of work per week for 3 randomly selected professors is more than 60 hours per week.

c) Why are your answers to the previous two questions different?

d) Could you have used a normal distribution to find an (approximate) probability for the average of 5 professors if the population of work hours did not have a normal distribution?

really need help on c &d if not all

wil vote thanks

Answer 1

Answers of part a and part b are correct.

c)

In part c, probability of sample mean is calculated while in part a probability of individual observation is calculated.

The standard deviation of sampling distribution is

Here sigma shows the population standard deviation.

So these answers are different.

d)

No since sample size 5 is very small. For this sample size, central limit theorem cannot be applied. So we cannot assume that sampling distribution of sample mean is normal.