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A bank auditor claims that credit card balances are normally distributed with mean $3000 and standard...

A bank auditor claims that credit card balances are normally distributed with mean $3000 and standard deviation $500. Suppose the auditor randomly select two card holders What is the probability both of them have card balances more than 2500?

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Answer #1

Mean = $3000

Standard Deviation = $500

z= (x-Mean)/ standard deviation

= (2500-3000)/500 = -1

From the z table, for z=-1, P(z<=-1) = 0.1587

P(Z>-1) = 1-0.1587 = 0.8413

For the two card holders, Probability = 0.8413*0.8413

= 0.708

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