In 2011 the scores of individual students on the ACT composite college entrance

Question

In 2011 the scores of individual students on the ACT composite college entrance exam had a normal distribution with mean 21.0 and standard deviation 5.2(based on the National Center of Education Statistics). a. If a student that took the ACT is randomly selected, what is the probability this student had a score greater than 27? b. Prestige College requires that a student have an ACT score in the top 25%. What is the minimum score a student could have in order to be accepted into Prestige College? In your own words; explain what a z-score describes and how it is related to the standard deviation. Also, explain what you know when the z-score is negative.

Explanation / Answer

8. Here mean=21 and sd=5.2

a. P(x>27)=P(z>27-21/5.2)=P(z>1.15)=0.1251

b. P(X>x)=0.25

so z=0.674=x-mean/sd

Hence x=0.674*5.2+21=24.5048

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