The LSAT has a mean score of 151 with a standard deviation of 9 and a unimodal,

Question

The LSAT has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 9 students at a time. A larger organization teaches class of 25 students at a time. Both organizations publish the mean scores of all their classes. a) What would you expect the distribution of mean class scores to be for each organization? b) If either organization has a graduating class with a mean score of 160, they'll take out a full-page ad in the local school paper to advertise. Which organization is more likely to have that success? Explain. c) Both organizations advertise that if any class has an average score below 145, they'll pay for everyone to retake the LSAT. Which organization is at greater risk to have to pay?

Explanation / Answer

a)   mean class score for the class with 9 students will follow a normal distribution with mean=151 and standard deviation = ( 9 / sqrt(9) =3..

mean class score for the class with 25 students will follow a normal distribution with mean=151 and standard deviation = ( 9 / sqrt(25) = 1.8..

b) for the class with 9 students..P [ mean score >= 160 ] = p [ z >= (160-151) / 3 ] = 0.001349898...
for the class with 25 students, .P [ mean score >= 160 ] = p [ z >= (160-151) / 1.8 ]=0.000000287...

so, the class with 9 students has the more of a chance .....

c)for the class with 9 studentts, P[ mean score < 145 ] = P [ z < (145-151) / 3 ] = 0.02275013...
for the class with 25 students, P[ mean score < 145 ] = P [ z < (145-151) / 1.8 ] = 0.0004290603...

So, the class with 9 students has the more risk too!

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