Question

6. A bank auditor claims that credit card balances are normally distributed, with a mean of $3570

Answer 1

Answer:

Probability that their mean credit card  balance is less than $2500 is 0.0073.

Step-by-step explanation:

We are given that a bank auditor claims that credit card balances are normally distributed, with a mean of $3570  and a standard deviation of $980.

You randomly select 5 credit card holders.

Let $\bar X$ = sample mean credit card balance

The z score probability distribution for sample mean is given by;

                                Z =  $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\mu$ = population mean credit card balance = $3570

            $\sigma$ = standard deviation = $980

            n = sample of credit card holders = 5

Now, the probability that their mean credit card  balance is less than $2500 is given by = P($\bar X$ < $2500)

    P($\bar X$ < $2500) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{2500-3570}{\frac{980}{\sqrt{5} } }$ ) = P(Z < -2.44) = 1 - P(Z $\leq$ 2.44)

                                                               = 1 - 0.9927 = 0.0073

The above probability is calculated by looking at the value of x = 2.44 in the z table which has an area of 0.9927.

Therefore, probability that their mean credit card  balance is less than $2500 is 0.0073.