Question

Use the normal distribution of SAT critical reading scores for which the mean is 506 and the standard deviation is 112. Assume the variable x is normally distributed. left parenthesis a right parenthesis What percent of the SAT verbal scores are less than 600​? left parenthesis b right parenthesis If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 525​?

Answer 1

Given,

= 506 , = 112

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( X < 600) = P( Z < 600 - 506 / 112)

= P( Z < 0.8393)

= 0.7993

b)

P( X > 525) = P( Z > 525 - 506 / 112)

= P( Z > 0.1696)

= 0.4327

Of the 1000 scores we expect 0.4327 * 1000 = 432.7 433 Scores greater than 525.