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# Normal Distribution

QUESTION: Example: Family incomes in two particular neighborhoods follow a normal distribution. For Neighborhood 1 the mean is \$26,500, with a standard deviation of \$15,000. For Neighborhood 2, the mean is \$30,000 with a standard deviation of \$18,000.

A) What proportion of families in Neighborhood 1 have incomes below the mean family income in Neighborhood 2?

B) What income level in Neighborhood 1 represents the top 10% for that neighborhood?

C) What income level for neighborhood 2 represents the lowest 5% of incomes for that neighborhoods?

D) For neighborhood 1, what percentage of families have incomes that fall between the mean incomes of Neighborhood 1 and neighborhood 2?

#### Solution Preview

M1 = 26 500 M2 = 30,000
<br>STD 1 = 15,000 STD 2 = 18,000
<br>
<br>A)P(X <= 30,000)where X is the THE PROPORTION whose fam income for neighborhood 1 is less than 30,000( MEan Income for neighborhood 2).
<br> Calculate the Z score; Z ...

\$2.19