The aptitude test scores of applicants to a university gradu

The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60. If the university wishes to set the cut-off score for graduate admission so that only the top 10 percent of applicants qualify for admission, what is the required cut-off score?

What percentage of applicants have test scores within two standard deviations of the mean?

Solution

The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60. If the university wishes to set the cut-off score for graduate admission so that only the top 10 percent of applicants qualify for admission, what is the required cut-off score?

Z score for top 10 % =1.282

x =mean+z*sd

x score for z=1.282, mean+z*sd

500+60*1.282=576.92

the required cut-off score=576.92

What percentage of applicants have test scores within two standard deviations of the mean?

95.44 % of the measurement in normal population lie with in the range of two standard deviations of the mean