Question

Use the normal distribution of SAT critical reading scores for which the mean is 503 and the standard deviation is 112. Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 650​? ( b) If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 575​?

(a) Approximately nothing​% of the SAT verbal scores are less than 650. ​(Round to two decimal places as​ needed.)

(b) If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 575​?

Answer 1

Answer:

Given that:

Use the normal distribution of SAT critical reading scores for which the mean is 503 and the standard deviation is 112.

Given information:

(a) Approximately nothing​% of the SAT verbal scores are less than 650

z-score for X = 650 is

So the percent of the SAT verbal scores are less than 650 is

P(X < 650) = P(z < 1.32)

= 0.9066

   = 90.66%

(b)  If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 575​?

z-score for X = 575 is

So the percent of the SAT verbal scores are greater than 575 is

P(X > 575) = P(z > 0.64)

= 0.2611

= 26.11%

So number of SAT verbal scores out of 1000 that you expect to be greater than 575 is 1000 * 0.2611 = 261.1 or 262.