Question

Assume that the following is true: THe scale for theSAT is set so that the distribution of scores is approximately normal with mean = 500 and standard deviation = 100.

You think that you might need a tutor. You know of a tutoring service for students who score between 350 and 650 on the SAT. You think that you probably fit within their range. What is the probability that you will get an SAT score between 350 and 650?

Answer 1

$\mu$ = 500

$\sigma$ = 100

To find P(350 < X < 650):

For X = 350:

Z = (350 - 500)/100

= - 1.50
By Technology, Cumulative Area Under Standard Normal Curve = 0.0668

For X = 650:

Z = (650 - 500)/100

= 1.50
By Technology, Cumulative Area Under Standard Normal Curve = 0.9332

So,

P(350 < X < 650) = 0.9332 - 0.0668 = 0.8664

So,

Answer is:

0.8664