Given that X is normally distributed with mean 100 and standard deviation 9 and given a sample size of 16, compute the following:

1) mean and variance of X-dash

2) P ( X-dash <= 98 )

3) P ( X-dash > 103 )

4) P ( 96 <= X-dash <= 102)

where X-dash is the sample mean.

My attempt so far:

I have used the formula

z = (X-dash - u) / (stdev(X-dash))

Where

X ~ N(u=100, s^2=9^2) and,

X-dash ~ N(u=100, s^2=81/16) <-- not sure about this one

and Since I am not sure about the variance of X-dash I can't continue to work out the appropriate critical values for z from the tables.

Help please with as much detail in the solution as possible so I can follow.

Cheers.