Suppose ACT Mathematics scores are normally distributed with

Suppose ACT Mathematics scores are normally distributed with a mean of 20.6 and a standard deviation of 5.5. A university plans to award scholarships to students whose scores are in the top 6%. What is the minimum score required for the scholarship? Please round your answer to the nearest tenth, if necessary.

Please show all of your work, steps, and calculatios. Explanations are greatly appreciated. Thank you.

Solution

P(X>x)=0.06

--> P((X-mean)/s <(x-20.6)/5.5) =1-0.06=0.94

--> P(Z<(x-20.6)/5.5) =0.94

--> (x-20.6)/5.5 = 1.55 (from standard normal table)

So x= 20.6 +1.55*5.5 =29.125