According to the Federal Reserve board the average credit ca

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 53,000.

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

Solution

a)

P(X<13000)=P(X-8565/53000 < 13000-8565/5300) =P(Z< 0.0836) =0.53

so aprrox 53%

Z is standard normal dist with (0.1)as parameter.

b)

P(X-8565/53000 <= K)=0.95

k=1.645

X-8565/53000 = 1.645

X=95750