The scores on the entrance exam at a well-known, exclusive law school are normal

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

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