Question

A leading magazine (dlike Barron's) reported at one time that the average number of weeks an individual is unemployed is 20.4 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 20.4 weeks and that the population standard deviation is 7.9 weeks. Suppose you would like to selecta random sample of 185 unemployed individuals for a follow-up study Find the probability that a single randomly selected value is between 19.3 and 21.2. 4 1120.9417 Find the probability that a sample of size Pl 19.3-. Af< 21.2)-|094171# -185 is randomly selected with a mean between 19.3 and 21.2. Enter your answers as numbers accurate to 4 decimal places

Answer 1

Solution

given : μ-20.4. σ 7.9, n 185

Pl-0.14 < Z < 0.10)

Required area under normal curve

$=P(Z<0.10)-P(Z<-0.14)$

$=0.5398-0.4443;mathbf{(from;z-table)}$

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P(-1.89 < Z < 1.38

Required area under normal curve

$=P(Z<1.38)-P(Z<-1.89)$

$=0.9162-0.0294;mathbf{(from;z-table)}$

0.8868