Question

Use the normal distribution of SAT critical reading scores for which the mean is 504 and the standard deviation is 112. Assume the variable x is normally distributed.
left parenthesis a right parenthesis

(a) What percent of the SAT verbal scores are less than 675​?
(b) If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 525​?

Approximately
_____% of the SAT verbal scores are less than 675.
​(Round to two decimal places as​ needed.)

Answer 1

a. Transform $X$, the random variable representing SAT scores, to $Z$, the same random variable but following the standard normal distribution, via

$X=\mu_XZ+\sigma_X$

$P(X$

so that about 93.77% of scores fall below 675.

b. Use the same strategy to compute $P(X>525)$:

$P(X>525)=P\left(\dfrac{X-504}{112}>\dfrac{525-504}{112}\right)\approx P(Z>0.1875)\approx0.5744$

Then out of 1000 scores, you would expect about 574 of them to exceed 525.