Question

Suppose x has a distribution with a mean of 70 and a standard deviation of 27. Random samples of size n = 36 are drawn.

(a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution ___________ with mean μx = _______ and standard deviation σx = __________.

(b) Find the z value corresponding to x = 79. z =

(c) Find P(x < 79). (Round your answer to four decimal places.) P(x < 79) =

Answer 1

(a)

By Central Limit Theorem,

x has distribution Normal with mean μx = 70 and standard deviation σx = 27/ = 4.5.

(b)

z value = (x - μx) / σx

= (79 - 70)/4.5

= 2

(c)

P(x < 79) = P(z < 2) = 0.9772 (Using Standard Normal Table)