Chapter 7, Problem 87H

$X\sim N$ (60, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ∑X be the random variable of sums. For parts c through f, sketch the graph, shade the region, Label and scale the horizontal axis for $\bar{X}$ and find the probability.

a. Sketch the distributions of X and $\bar{X}$ on the same graph.

b. $\bar{X}\sim$ ___(__ ,__ )

c. P(x < 60) ___ .

d. Find the 30^th percentile for the mean.

e. P(56< x < 62)= .

f. P(18< x < 58)=

h. Find the minimum value for the upper quartile for the sum.

i. P (1,400 < ∑ x: 1,550) = _____.