I need to do these problems in excel. i need the excel formulas. 3. The average

Question

I need to do these problems in excel. i need the excel formulas.

3. The average ACT score for first-time students entering the University of Alabama has shown an increasing trend during the past several years. The average score was 25.9 for the Fall 2012 semester. Let’s assume that the ACT score data for Fall 2012 can be described as a normal distribution, and that the standard deviation is 6.0. Suppose one of the Fall 2012 entering students is selected at random. Determine the following.

(a) The probability the randomly selected student’s score is 30 or more.

(b) The probability the randomly selected student’s score is less than 20.

(c) The probability the randomly selected student’s score is in the 20s.

(d) Suppose your ACT score is 22. Determine your percentile.

(e) What would your ACT score have to be in order to be in the 90th percentile?

Explanation / Answer

a) here P(X>30) =1-P(X<30) =1-norm.dist(30,25.9,6,true) =0.2472

b)P(X<20)= norm.dist(20,25.9,6,true)=0.1627

c)P(20<X<29)=norm.dist(29,25.9,6,true)-norm.dist(20,25.9,6,true)=0.5346

d)percentile =norm.dist(22,25.9,6,true)*100 =25.78 th percentile

e) 90th percentie =norm.inv(0.9,25.9,6)=33.5893

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