Homework Sourse3 The math SAT scores for all women are normally distributed
3. The math SAT scores for all women are normally distributed with a mean of 496 and a standard deviation of 108.
If a woman who takes the math portion of the SAT is randomly selected, find the probability that her score is above 500.
If five math SAT scores are randomly selected from the population of women who take the test, find the probability that all five of the scores are above 500. (Remember the Multiplication Rule from Chap 4)
If five women who take the math portion of the SAT are randomly selected, find the probability that their mean score is above 500.
Find P90, the score separating the bottom 90% from the top 10%.
Solution
a. If a woman who takes the math portion of the SAT is randomly selected, find the probability that her score is above 500.
Normal cdf (lower, upper, mean, standard deviation).
(500, 1099, 496, 108)
=.4852
b. If five math SAT scores are randomly selected from the population of women who take the test, find the probability that all five of the scores are above 500. (Remember the Multiplication Rule from Chap 4)
0.4852^5 = 0.0269
c. If five women who take the math portion of the SAT are randomly selected, find the probability that their mean score is above 500 (use central limit theorem).
=.9172
d. Find P90, the score separating the bottom 90% from the top 10%.
invNorm (.90,496,108)= 634.4075692 ---> ~634.41
