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.