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U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790\$ 7,790 (Kiplinger's, August 2007). Assume that the average amount spent on a debit card is normally distributed with a standard deviation of $500\$ 500.

c. Compute the 75 th percentile of the amount spent on a debit card.

Solution

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Answered 7 months ago
Answered 7 months ago
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c) We have to determine xx so that P(X<x)=0.75P(X<x)=0.75.

Use Eq. (2)(2) to convert to Z=(X7790)/500Z=(X-7790)/500 and we have:

P(X<x)=0.75=P(Z<x7790500).\begin{align*} P(X<x)&=0.75=P\left(Z<\dfrac{x-7790}{500}\right). \end{align*}

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