Answer to Question #161473 in Statistics and Probability for Allison

Question

In a job fair, 3000 aspirants applied for a job. The mean age was found to be 28 years with a standard deviation of 4years?

i)how many applicants are 33 years old and below?

ii)how many applicants are 21 years old and above?

iii)how many have aged between 24 and 30 years?

Answer 1

I. $P(x\le33)$

$P(X\le33)=P(Z\le\frac{33-28}{4})$

$=P(Z\le\frac{5}{4})=0.8944$

II. $P(X\ge21)$

$P(X\ge21)=1-P(Z\le\frac{21-28}{4})$

$=1-P(Z\le\frac{-7}{4})=0.9599$

III. $P(24\le X\le30)$

$P(24\le X\le30)=P(\frac{24-28}{4}\le Z\le\frac{30-28}{4})$

$=P(-1\le Z\le0.5)=0.533$