Question

A bank has 175 000 credit card holders. During one month the average

amount spent by each card holder totalled $192,50 with a standard deviation

of $60,20. Assuming a normal distribution, determine the number of card holders who spent more than $250.

Answer 1

Solution:

$\mu=192.50,\sigma=60.20$

$X\sim N(\mu,\sigma^2)$

$P(X>250)=1-P(X\le250) \\=1-P(z\le\dfrac{250-192.50}{60.20}) \\=1-P(z\le0.96) \\=1-0.83147 \\=0.16853$

Required number of credit cards holders$=175000\times 0.16853=29492.75$