SOLUTION: The results of the latest writing of the LSAT (Law School Aptitude Test) showed results that were normally distributed with a mean score of 829 and a standard deviation of 50. T

Question 1186035: The results of the latest writing of the LSAT (Law School Aptitude Test) showed results that were normally distributed with a mean score of 829 and a standard deviation of 50.
The Osgoode Hall Law School wants candidates for admission to be in the top 1
%
of LSAT test scores. What is the minimum test score a candidate needs to achieve to be considered for admission to this school?

If a group of 42 applicants is randomly selected, what is the probability that the group average is not less than 849?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
men of the population is 829
standard deviation of the population is 50.

critical z-score for admission to be in the top 1 percent is equal to 2.326348 rounded to 6 decimal places.

z-score formula is:

z = (x - m) / s

z is the z-score
x is the individual score
m is the mean
s is the standard deviation

the critical z-score formula becomes:

2.326348 = (x - 829) / 50.

solve for x to get:

x = 2.326348 * 50 + 829 = 945.3174.

sample size = 42.

when you're dealing with the mean of a sample, rather than an individual score, you need to use the standard error.

standard error = standard deviation / square root of sample size = 50 / sqrt(42) = 7.715167 rounded to 6 decimal places.

z = (x - m) / s

z is the z-score
x is the sample mean
m is the population mean
s is the standard error

formula becomes:

z = (849 - 829) / 7.715167 = 2.5923 rounded to 4 decimal places.

area to the right of that z-score is equal to .00477 rounded to 5 decimal places.

that's the probability that the group average is not less than 849.

i used the following calculator to confirm these results are accurate, assuming i calculated the standard error correctly.

https://www.statskingdom.com/normal.html

the results from the use of that calculator are shown below.

minimum score for top 1%:

probability of sample mean not less than 849.

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