Hi.

I'm having a little problem solving this one.

Let X(bar) and S^2 denote the sample mean and sample variance in random sampling, sample size 20 from a N(10,80) distribution population. Calculate the probabilities of the following events.

10<= X(bar) <= 12, S^2 <= 108.8

Z= (X(bar)-10/(root(80/20))

Since X(bar) ~ (u, sigma^2/n), 10-10/(root(80/20) <= Z <= 12-10 / (root(80/20)

0 <= Z<= 1

19S^2/80 <= 10.8*19/80 ~ Chi-square (19)

Now how do I find the common area between the two events?

Also how should I approach

X(bar) <= 10 + 0.2037S

Thanks.