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 853 and a standard deviation of 100.

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Question 1167660: The results of the latest writing of the LSAT (Law School Aptitude Test) showed results that were normally distributed with a mean score of 853 and a standard deviation of 100.
Enter percentage answers in percent form (i.e. 3.00 % instead of 0.03). Round all final answers to 2 decimals.
(a) What percent of students scored between 729 and 1021? %

(b) What percent of students got 995 or more on the test? %

(c) The Osgoode Hall Law School wants candidates for admission to be in the top 2 % of LSAT test scores. What is the minimum test score a candidate needs to achieve to be considered for admission to this school?

For part (d) enter probability answers in decimal form (i.e. 0.0003 instead of 0.0300 %). Round the final answer to 4 decimals.
(d) If a group of 41 applicants is randomly selected, what is the probability that the group average is not less than 873?
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd
=(729-853)/100=-1.24
and (1021-853)/100=+1.68
probability is z between those two values, which is 84.60%
greater than 995 is z>1.42 or probability 7.78%
top 2% is z of 2.05
this would therefore be 205 more than the mean or 1058.
look at 873 z=(873-853)/100/sqrt(41)=20*sqrt(41)/100 or 1.28. Not less than 873 is z>1.28 which is 0.1003.