Question

# 25. Use the normal distribution of SAT critical reading scores for which the mean is 503...

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.)

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

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