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Allisa [31]
2 years ago
12

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

Mathematics
1 answer:
sergejj [24]2 years ago
4 0

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<em> </em>\bar X<em> = </em><u><em>sample mean credit card balance</em></u>

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<em> </em>< $2500)

    P(\bar X<em> </em>< $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.

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