Mathematical Statistics Xi~N(6,25) P[1.860 < 3(Xbar - 6]/S

[cimmerian]

Homework Statement

Let X1, X2, ..., X9 be a random sample from a normal distribution, Xi~N(6,25), and denote by Xbar and S^2 the sample mean and sample variance. Use the standard statistical table for normal distribution.

Homework Equations

E[S^2] = δ^2 = 25

S^2 = (ƩXi^2 - nXbar^2)/(n-1)

The Attempt at a Solution

I have to find the probability and I want to move Xbar to one side. To do that, I need to find the value of S. I have no idea how to do this. I don't know how to use the sum. All I know is that n=9. I got a very complicated integral from using E[S^2]. How do I find S? Or what should I do if I can't?

 

[Ray Vickson]

Homework Statement

Let X1, X2, ..., X9 be a random sample from a normal distribution, Xi~N(6,25), and denote by Xbar and S^2 the sample mean and sample variance. Use the standard statistical table for normal distribution.

Homework Equations

E[S^2] = δ^2 = 25

S^2 = (ƩXi^2 - nXbar^2)/(n-1)

The Attempt at a Solution

I have to find the probability and I want to move Xbar to one side. To do that, I need to find the value of S. I have no idea how to do this. I don't know how to use the sum. All I know is that n=9. I got a very complicated integral from using E[S^2]. How do I find S? Or what should I do if I can't?

Look up the "Student's t-distribution".

RGV