Quandaries and Queries


My name: Gary
I'm a student.
The level of the question: secondary (10-12).

I have the following questions which I can not answer:

In a law school class, the entering students averaged about 160 on the last
LSAT; the standard deviation was about 8. The historgram of the lLSAT
scores follwed the normal curve reasonable well.

Q. About what percentage of the class scored below 166?

Q. One student was 0.5 above average on the last LSAT, about what percentage
of the students had lower scores than he did?

Thanks for your help.




Hi Gary,

Since the histogram showed approximately a normal distribution you are expected to assume that the distributioin is normal with mean 160 and standard deviation 8. If X is the random variable that is the score of a student on the test then the percentage of the class that scored below 166 is

Pr(X < 166)

Since you are to assume that X is normal with mean 160 and standard deviation 8 you can convert this to a probability concerning the standard normal variable Z by using the transformation

Z = (X - mean)/standard deviation

Thus the probability becomes

Pr(X < 166) = Pr(Z < (166 - 160)/8)

Use the standard normal tables to calculate this probability.

For the second part you can use the same method to find

Pr(X < (160 + 0.5)) = Pr(X < 160.5)



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