Question

Uptown Country Club only admits members with annual incomes in the top 2.5% of the United States. If the annual individual income in the US has a mound-shaped symmetrical distribution with a mean of $55,000 and a standard deviation of $10,000, what is the approximate minimum annual income required for admission to the country club?

Answer 1

$74,600

Explanation:

-Given the probability is 2.5%, mean=$55,000 and standard deviation= $10,000

-We find the z value of 2.5%

`p=P(z>(X-\mu)/(\sigma))\\\\1.96=P(z<(X-\mu)/(\sigma)}\\\\\\\therefore 1.96=(X-55000)/(10000)\\\\\\X=1.96* 10000+55000\\\\=74600`

Hence, the minimum amount of income to be in the top 2.5% is $74,600