The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 200 and a standard deviation equal to 50. 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.)

Question

Mathematics

Frau Frau

6 July, 18:06

The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 200 and a standard deviation equal to 50. 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.)

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Answers (1)

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Hezekiah · Answer 1

the lowest passing score would be x = 298

Step-by-step explanation:

School wishes that only 2.5 percent of students taking test pass

We are given

mean = 200,

standard deviation = 50

We need to find x

The area under the curve can be found by:

2.5 % = 0.025

So, 1 - 0.025 = 0.975

We need to find the value of z for which the answer is 0.975

Looking at the z-score table, the value of z is: 1.96

Now, using the formula:

z = x - mean/standard deviation

1.96 = x - 200/50

=> 1.96 * 50 = x-200

98 = x - 200

=> x = 200+98

x = 298

So, the lowest passing score would be x = 298