At a large university an exam is used to evaluate the quantitative skills of inc

Question

At a large university an exam is used to evaluate the quantitative skills of incoming freshmen. Historically the scores have been normally distributed with a mean mu = 72.5 and a standard deviation sigma = 11. a) Students who receive a score of below 55 are required to take a supplemental course to help Improve their quantitative skills. What percent of Incoming freshmen would be required to take this supplemental course? b) A student with a score of above 90 is allowed to take an advanced math course. What percent of incoming freshmen are permitted to take the advanced math course? c) What percent of the incoming freshmen have a score between 55 and 90?

Explanation / Answer

(1)
mean = 72.5
std. dev. = 11

(a)
P(X<55) = P(z<(55-72.5)/11) = P(z<-1.5909) = 0.0558

Hence 5.6% of incoming freshmen would be required to take this supplement course.

(b))
P(X>90) = P(z>(90-72.5)/11) = P(z>1.5909) = 0.0558

Hence 5.6% of incoming freshmen are permitted to take the advanced math course.

(c)
P(55<X<90) = P(-1.5909 < z < 1.5909) = 1 - 2*0.0558 = 0.8884

Hence 88.8% of the freshment have a score between 55 and 90.

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