Question

Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500.

a. What minimum income does a household need to earn to be in the top 5% of incomes?

b. What maximum income does a household need to earn to be in the bottom 40% of incomes?

Answer 1

a)

mean μ=55000standard deviation σ=4500.0000for 95th percentile critical value of z=1.645

therefore corresponding

value=mean +z$\times$ std deviation=62402.50

therefore  minimum income does a household need to earn to be in the top 5% of incomes =62402.50

b). The maximum income does a household needs to earn to be in the bottom 40% of incomes is calculated by finding the Z score at the bottom 40th percentile using excel formula =NORM.S.INV(0.40), thus the Z score is computed as -0.2533.

Now using the Z score computational formula the X score is calculated as:

value=mean +z$\times$ std deviation = 53860.15

Thus the maximum score will be $ 53860.15.