The mean spent on lottery tickets is normally distributed with a mean of $6.50 and a standard deviation of $2.25. If one customer is randomly selected, find the probability they will spend between $4 and $9.50

First, we have to find the z scores of $4 and $9.50.

Z₁ = ($4 - $6.50) / $2.25 = - 1.11

Z₂ = ($9.50 - $6.50) / $2.25 = 1.33

Then, using a z score table, we find the probability of 1.33 and - 1.11, and subtract them to determine the probability in between.

0.9082 - 0.1335 = 0.7747 or 77.47%.