Question

Given X ~ U(2, 27). Suppose that you form random samples of size 8 from this distribution. Answer the following, rounding probabilities to 4 decimals and everything else to 2 decimals..

a. The average of X-bar is and the standard deviation of X-bar is

For the following, use the average and standard deviation found in part a.

b. Find P(12 < X-bar < 14.5). d. Find the 72nd percentile of X-bar.

Answer 1

a)

Here X~U(2,27). So,

Using Normal approximation to Uniform distribution,

From Central Limit Theorem, we know

So,

b)

Now,

Let 'x' be the 72th percentile of . Then,

Using probability tables, we have