Question

1. The distribution of SAT scores in math for an incoming class of business students has a mean of 610 and standard deviation of 20. Assume that the scores are normally distributed.
   1. Find the probability that an individual’s SAT score is less than 600.
   2. Find the probability that an individual’s SAT score is between 590 and 620.
   3. Find the probability that an individual’s SAT score is greater than 650.
   4. What score will the top 5% of students have?

Answer 1

Given,

mean = 610, Standard deviation = 20

a.Individual SAT score is less then 600 i.e., p(x<600)

  

p(z<-0.5) = 1 - p(z>0.5) =1 -0.6915 ..by using Statistical Table

=0.3085

b.Individual SAT score between 590 to 620.

p(-1 < z < 0.5) = 1 - p(z>1) - p(z>0.5)

= 1- 0.15866 -0.30854 ...by using statistical table

=0.5328

c.Individual SAT score is greater than 650.

  

then p(z>2) = 0.02275 ... by using statistical table

d.Top 5% students score

p(Z>z)=0.05

p(1.64>z)=0.05 ...by using statistical table

Hence, Top 5% students score is 642.89