Question

- 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.
- Find the probability that an individual’s SAT score is less than 600.
- Find the probability that an individual’s SAT score is between 590 and 620.
- Find the probability that an individual’s SAT score is greater than 650.
- 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

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