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Question

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 $\$ 7,790$ (Kiplinger's, August 2007). Assume that the average amount spent on a debit card is normally distributed with a standard deviation of $\$ 500$.

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

Solution

VerifiedAnswered 7 months ago

Answered 7 months ago

Step 1

1 of 5c) We have to determine $x$ so that $P(X<x)=0.75$.

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

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

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