The NCAA requires Division-I athletes to score at least 850 on the combined math

Question

The NCAA requires Division-I athletes to score at least 850 on the combined mathematics and verbal parts of the SAT exam in order to compete in their first college year. In 2000, the scores of the more than one million students taking the SATs were approximately normal with 1019 and standard deviation of 209. What percent of all students had SAT scores of at least 850? this = 79.06% can someone help with part b which is

1b. The NCAA considers a student a “partial qualifier” eligible to practice and receive an athletic scholarship, but not to compete, if the combined SAT score is at least 730. What percent of all students who take the SAT would be partial qualifiers?

Explanation / Answer

From given information, mu=1019, sigma=209. Compute the following probability by substituting values in Z score formula.

P(X>=730)=1-P(X<730)=1-P[Z<=729]=1-P[Z<=(729-1019)/209] [Z=(X-mu)/sigma, where, X is the raw score, mu is population mean, and sigma is population standard deviation]

=1-P(Z<=-1.39)

=1-0.0823 [find area corresponding to the Z score in the Z table, the table gives area under standard normal curve to the left of Z]

=0.9177

Now mutiply 0.9177 with 100 to obtain the percent of all students who take SAT to be partial qualifier.

Ans>91.77%

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