Question

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1546 and a standard deviation of 296. The local college includes a minimum score of 954 in its admission requirements.

What percentage of students from this school earn scores that satisfy the admission requirement?
P(X > 954) =  %

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign).

Please provide a step-by-step so I can practice this problem on my own! Thank you.

Answer 1

Let ,

Now , we want to find the P(X>954)

Therefore ,

; Since , the normal distribution is symmetric, i.e. P(Z>a)=P(Z<-a)

; From the normal probability integral table

Therefore , 97.73% of students from this school earn scores that satisfy the admission requirement.