Question

25. Use the normal distribution of SAT critical reading scores for which the mean is 503 and the standard deviation is 110. Assume the variable x is normally distributed. left parenthesis a right parenthesis What percent of the SAT verbal scores are less than 675​? left parenthesis b right parenthesis If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 525​? left parenthesis a right parenthesis Approximately nothing​% of the SAT verbal scores are less than 675. ​(Round to two decimal places as​ needed.)

Answer 1

a) P(X < 675)

= P((X - )/ < (675 - )/)

= P(Z < (675 - 503)/110)

= P(Z < 1.56)

= 0.9406 = 94.06%

b) P(X > 525)

= P((X - )/ > (525 - )/)

= P(Z > (525 - 503)/110)

= P(Z > 0.2)

= 1 - P(Z < 0.2)

= 1 - 0.5793

= 0.4207

Expected number of SAT verbal scores = 1000 * 0.4207 = 420.7 = 421