If 75% of men spend more than $75 monthly on clothes, while 15% pay more than $150, what is the mean monthly expense on clothes
and what is the standard deviation? \mu=84.33, \sigma=13.44
\mu=104.39, \sigma=43.86
\mu=118.42, \sigma=56.16
\mu=139.43, \sigma=83.36
\mu=54.43, \sigma=13.22
We are given that 75% of men spend more than $75 on clothes, while 15% of men spend more than $150.
To solve this problem, we assume the mean =m, and standard deviation = s.
Then P(X>75)=1-P(X<75)=0.75=1-P((75-m)/s<75)=0.75 (75-m)/s=Z(P=1-0.75)=-0.6744898 [ last value from tables ] giving equation 75-m=-0.6744898s........................(1)
Similarly P(X>150)=1-P(X<150)=0.15=1-P((150-m)/s<150)=0.15 (150-m)/s=Z(P=(1-0.15)=1.036433 or 150-m=1.036433s..........................(2)
Solving the system of equations (1) and (2) for m and s gives m=104.57 s=43.84 which is exactly what we need. Substitute mu=m, and sigma=s allows you to find the answer choice.
