Thread: find sample mean and S.D

Suppose a random sample of n=36 observations is selected from a population that has normal distribution with mean 106 and standard deviation 12.

a) Give the mean and the standard deviation of the sample mean X bar.

b) find the probability that X bar exceeds 108.

c) Find the probability that the sample mean deviates from the population mean by less than 3.


I dun quite understand part a and part c, isn't the sample mean same a the population mean? How about the standard deviation, which formula shud I use?

For part b, I use P(X bar >= 108)= P(z>=108-106/(12/square root of 30)), is this correct?

Part b) looks good but 36 is in the square root, not 30.

For part a)

Originally Posted by pickslides

Part b) looks good but 36 is in the square root, not 30.

For part a)

thanks a lot, so for part c, do I just follow part b to find: P(z<3)=p(<=2)?