Question

Use the normal distribution of SAT critical reading scores for which the mean is 502 and the standard deviation is 116. Assume the variable x is normally distributed. left parenthesis a right parenthesis(a) What percent of the SAT verbal scores are less than 675? left parenthesis b right parenthesis(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575? left parenthesis a right parenthesis(a) Approximately nothing% of the SAT verbal scores are less than 675. (Round to two decimal places as needed.)

Answer 1

(a) 93.19%

(b) 267.3

Explanation:

The population mean and standard deviation are given as 502 and 116 respectively.

Consider, X be the random variable that shows the SAT critical reading score is normally distributed.

(a) The percent of the SAT verbal scores are less than 675 can be calculated as:

`P(X<675)=P(Z<(675-502)/(116))\\ P(X<675)=P(Z<(675-502)/(116))\\P(X<675)=P(Z<1.49)\\P(X<675)= 0.9319`

Thus, the required percentage is 93.19%

(b)

The number of SAT verbal scores that are expected to be greater than 575 can be calculated as:

`P(X>575)=P((x-502)/(116)>(575-502)/(116)\\P(X>575)=P(Z>(575-502)/(116))\\P(X>575)=P(Z>0.6293)\\P(X>575)=0.2673`

So,

Out of 1000 randomly selected SAT verbal scores, 1000(0.2673) = 267.3 are expected to have greater than 575.