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?