In year 2003. the SAT test scores were normally distributed with a mean of 1180

Question

In year 2003. the SAT test scores were normally distributed with a mean of 1180 and a standard deviation of 120. Answering the following questions: a). What is the probability that a randomly selected student's SAT score is between 1030 and 1280? b). What SAT score should a student have in order to be considered by an Ivy League College which only considers those whose SAT scores arc in the top 5%? c). What is the probability that a randomly selected student's SAT score is exactly 1170? d). What is the probability that a randomly selected student's SAT score is at least 1500? e). If 2050 students scored at least 1500. estimate how many students took the SAT exam in that year?

Explanation / Answer

Part-a

P(1030<X<1280)=0.6920

This is using excel function =NORMDIST(1280,1180,120,TRUE)-NORMDIST(1030,1180,120,TRUE)

Part-b

We have to find x0 such that P(X<x0)=0.95

So, x0= 1377.38 using following excel function

=NORMINV(0.95,1180,120)

Part-c

P(X=1170)=0 as for continuous distributions probability at a single point is zero.

Part-d

P(X>=1500)= 0.0038 using following excel function

=1-NORMDIST(1500,1180,120,TRUE)

Part-e

Number of students who took SAT exam1 =x say

Then 2050/x=0.0038

So, x=2050/0.0038=539473.6842539474

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