The aptitude test scores of applicants to a university graduate program are norm

Question

The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60. a) Applicants need a test score higher than 530 to be admitted into the graduate program. What proportion of applications qualify? b) If the university wishes to set the cutoff score for graduate admission so that only the top 10% of applicants qualify for admission, what is the required cutoff score? c) What percentage of applicants have test scores within two standard deviations of the mean?

Explanation / Answer

a) P(X>530)=1-P(X<50)=1-NORM.DIST(530,500,60,TRUE)=1-0.6915=0.3085.

b) NORM.INV(0.1,500,60)=423.1069

c) using the probability rule, 95% of the scores fall within two sds from the mean.

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