Question

Given that X ~ N(120, 35). We survey samples of 25 and are interested in the distribution of X-bar. Find the z-score associated with x-bar = 100.

a. -14.2857
b. -20/35
c. -2.8571
d. -20

Answer 1

Option c -2.8571

Explanation:

z-score are calculated as

`z=(xbar-mean)/((S.D)/(√(n) ) )`.

We are given that mean=120 and standard deviation=S.D=35 as X~N(120,35).

Sample size=n=25.

We have to find z-score for x-bar=100. So,

z-score=[100-120]/[35/√25]

z-score=[-20]/[35/5]

z-score=-20/7

z-score=-2.8571.

Thus, the z-score associated with x-bar = 100 is -2.8571.