Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 38 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 38 weeks and that the population standard deviation is 6 weeks. Suppose you would like to select a random sample of 35 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is less than 39. X<39)0.8389 Find the probability that a sample of size n 35 is randomly selected with a mean less than 39. P(M<39)-0.8389 Enter your answers as numbers accurate to 4 decimal places

Answer 1

(a)

$\mu$ = 38

$\sigma$ = 6

To find P(X<39):

Z = (39 - 38)/6 = 0.1667

Table of Area Under Standard Normal Curve gives area = 0.0675

So,

P(X<39) =0.5 +0.0675 = 0.5675

So,

Answer is:

0.5675

(b)

$\mu$ = 38

$\sigma$ = 6

n = 35

SE = $\sigma$ /$\sqrt{n}$

= 6/ = 1.0142

To find P(M<39):

Z = (39 - 38)/1.0142 = 0.9860

Table of Area Under Standard Normal Curve gives area = 0.3389

So,

P(X<39) =0.5 +0.3389 = 0.8389

So,

Answer is:

0.8389