Credit card balances are normally distributed with a mean of exist3245 and a sta

Question

Credit card balances are normally distributed with a mean of exist3245 and a standard deviation, sigma = exist340. a) What is the probability that a randomly selected credit card holder has a credit card balance greater than exist2750? b) You randomly select 25 credit card holders. What is the probability that their mean credit card balance is greater than exist2750? c) Since credit card debt can lead to other serious financial issues, financial analysts feel that people should have credit card balances at the bottom 15%. What amount of credit card debt is this associated with?

Explanation / Answer

a)

P(X > 2750) = P(Z > 2750 - 3245 / 340)

= P(Z > -1.4559)

= 0.9273

b)

P(Z > 2750) = P(Z > 2750 - 3245/340/sqrt(25))

= P(Z > -7.2794)

= 1

c)

P(X < x) = 0.15

=>

x - mean/std = invnorm(0.15)

=>

x - 3245 / 340 = -1.036

=>

x = 3597.24

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