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1. For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 520 with a standard deviation of 100. SAT scores are normally distributed.
a. What is the probability that a randomly selected high school senior's score on the mathematics part of the SAT will be more than 676?
b. What is the probability that a randomly selected high school senior's score on the mathematics part of the SAT will be less than 403?
c. What is the probability that a randomly selected high school senior's score on the mathematics part of the SAT will be between 403 and 676?
d. Suppose that an engineering school honors program will accept only high seniors with a mathematics SAT score in the top 15%. What is the minimum SAT score in mathematics for this program?
e. Suppose that an engineering school honors program will accept only high seniors with a mathematics SAT score in the top 25%. What is the minimum SAT score in mathematics for this program?
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