# Math Help - Normal Distribution Problem

1. ## Normal Distribution Problem

A large computer chip manufacturing plant under construction in Westbank is expected to add 1400 children to the county's public school system once the permanent work force arrives. Any child with an IQ under 80 or over 135 will require individualized instruction that will cost the city an additional \$1750 per year. How much money should Westbank anticipate spending next year to meet the needs of its new special ed students? Assume that IQ scores are normally distributed with a mean of 100 and a standard deviation of 16.

2. Find $pr(X<80)$ and $pr(X>135)$, where X= a student's IQ Score.

Take those two probabilities and multiply each by the number of students that will be added to the school district. This will give you the number of students who have an IQ lower than 80 or higher than 135.

$pr(X<80) * 1,400$ and $pr(X>135) * 1,400$

Now, just sum those two numbers and multiply them by additional cost that individualized instruction will be. This will give you the total amount of money that the city will have to set aside.

Sum $* \1,750$