The scores on the entrance exam at a well-known, exclusive law school are normal
ID: 3063967 • Letter: T
Question
The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 264 and a standard deviation equal to 36. At what value should the lowest passing score be set if the school wishes only 2.5 percent of those taking the test to pass? (Round your answer to nearest whole number.)
The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 264 and a standard deviation equal to 36. At what value should the lowest passing score be set if the school wishes only 2.5 percent of those taking the test to pass? (Round your answer to nearest whole number.)
Explanation / Answer
Let A be the lowest passing score
P(X < A) = P(Z < (A - mean)/standard deviation)
Mean = 264
Standard deviation = 36
P(X > A) = 2.5% = 0.025
P(X < A) = 1 - 0.025 = 0.975
P(Z < (A - 264)/36) = 0.975
Take the value of z corresponding to 0.975 from the standard normal distribution table
(A - 264)/36 = 1.96
A = 334.56
Set lowest passing score to 335