According to the Federal Reserve board, the average credit card debt per U.S. ho

Question

According to the Federal Reserve board, the average credit card debt per U.S. household was $ 8,565 in 2008. Assume that the distribution of credit card debtper household has a normal distribution with a standard deviation of 3,000.

a) Determine the percentage of households that have a credit card debt of less than $13,000

b) One household has a credit card debt that is at the 95th percentile. Determine its credit card debt

d) Determine the percentage of households that have a credit card debt between 11000 and 12500

e) Is there a household that have a credit card debt of more than 22000? Explain?

Explanation / Answer

P(X>13000) = P((X-mean)/s >(13000-8565)/3000)

=P(Z>1.48)=0.0694 (from standard normal table)

P(X<c)=0.95

--> P(Z<(c-8565)/3000)=0.95

--> (c-8565)/3000 = 1.64 (from standard normal table)

--> c= 8565 +1.64*3000=13485

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