Answer to Question #230458 in Statistics and Probability for Jamilah

Question

b) 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 hold￾ers who spent more than $250

Answer 1

By condition,

$a = 192.5,\,\,\sigma = 60.2$

Let's find the probability

$P(x > 250) = \Phi \left( \infty \right) - \Phi \left( {\frac{{250 - a}}{\sigma }} \right) = 0.5 - \Phi \left( {\frac{{250 - 192.5}}{{60.2}}} \right) = 0.5 - \Phi \left( {0.96} \right) \approx 0.5 - 0.3315 = 0.1685$

Since

$0.1685 \cdot 175000 = {\rm{29487}}{\rm{.5}}$

Then the wanted number is 29487 (this number must be an integer)

Answer: 29487