Answer to Question #308326 in Statistics and Probability for Zem

Question

V.

In a job fair, 2000 applicants applied for a job. Their main age was found to be 28 with a standard deviation of 4 years.

a. Draw a normal curve distribution showing the z-scores and the raw scores

b. How many applicants are below 20 years old?

c. How many applicants are above 30 years old?

d. How many have ages between 24 and 32 years old?

Answer 1

b) $\mu=28,\sigma=4,n=2000,Z=(x-μ)/σ$

$P(x<20)=P(Z<(20-28)/4)=P(Z<-2)$

$P(Z<-2)=0.0228$

Number of applicants = $2000×0.0228=45.6$

Thus approximately 46 applicants

c) $P(X>30)=P(Z>(30-28)/4)=P(Z>0.5)$

$=1-P(Z<0.5)=1-0.6915=0.3085$

Number of applicants $=2000×0.3085=617$

d) $P(24<x<32)=P((24-28)/4<Z<(32-28)/4)=P(-1<Z<1)$

$=P(Z<1)-P(Z<-1)$

$=0.8413-0.1587$

$=0.6826$

Number of applicants $=2000×0.6826=1365.2$

Thus approximately 1365 applicants.