Question

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

Answer 1

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.