Question

In June 2012, the average Amercian credit card account balance was US$3,127.

Assuming that these balances are approximately normally distributed with a mean of US$3,127 and a standard deviation of US$1,500:

a) P(that an account balance is less than $2,500).

(Use diagram to show.)

b) one quarter of credit card accounts carry at least what balance? (Use diagram to Show)

Answer 1

a)

The following is obtained graphically:

b)

We know that X is normally distributed, with parameters:

We need to find a score x so that the corresponding cumulative normal probability is equal to 0.25. Mathematically, x is such that:

The corresponding z score so that the cumulative standard normal probability distribution is 0.25 is

zc​=-0.6745

This value of zc​=-0.6745 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.25 cumulative probability is

The following is obtained graphically:

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