The heights of women aged 20 to 29 follows approximately the N(64, 2.8) distribu
ID: 3270462 • Letter: T
Question
The heights of women aged 20 to 29 follows approximately the N(64, 2.8) distribution. Men the same age have heights distributed as N(69.3, 2.7). What percent of young women are taller than the mean height of young men? _____ % Changing the mean and standard deviation of a Normal distribution by a moderate amount can greatly change the percent of observation in the tails. Suppose that a college is looking for applicants with SAT math scores 740 and above. a) In 2007, the scores of men on the math SAT followed the N(533, 116) distribution. What percent of men scored 740 or better? = _____ % b) Women's SAT math scores that year had the N(499, 110) distribution. What percent of women scored 740 or better? = _____ %Explanation / Answer
1.
Mean Height of young men = 69.3
Percent of young women taller than mean height of young women = P(X > 69.3)
= P[Z > (69.3 - 64)/2.8] = P(Z > 1.893) = 0.0292 (Using Z table calculator)
= 2.92 %
2.
(a) Percent of mean scored 740 or better by men = P(X > 740)
= P[Z > (740-533)/116] = P(Z > 1.7845) = 0.0372 (Using Z table calculator)
= 3.72%
(b) Percent of mean scored 740 or better by women = P(Y > 740)
= P[Z > (740-499)/110] = P(Z > 2.191) = 0.0142 (Using Z table calculator)
= 1.42%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.