Southern University gives an entrance exam to all candidates seeking admission t

Question

Southern University gives an entrance exam to all candidates seeking admission to the university. In 2006, a total of 1, 500 students applied for admission to the university. Over the years, the mean test score is 86 with a standard deviation of 16. To help determine how many students are likely to gain admission, a sample of 75 applicants that took the test were used for the study. To be accepted, the score must be greater than 84. In 2006, what percent of the 1, 500 students are likely to gain entrance into Southern University?

Explanation / Answer

from normal distribution z=(X-mean)/std deviation

hence probabilty to have a score greater then 84 =P(X>84)=1-P(X<84)=1-P(Z<(84-86)/16)=1-P(Z<-0.125)

=1-0.4503=0.5497

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