Admission to a certain university is determined by an entry exam. The scores of this test are Normally distributed with a mean of 400 and a standard deviation of 60. Only students who score in the top 30% will be offered admission. Amy scores 425 on the test. Choose the most accurate statement? A) The top 30% is defined with a score less than or equal to 431.4 so she will be admitted. B) The top 30% of all students have scores greater than or equal to 520 so she will not be admitted. C) The top 30% of all students have scores greater than or equal to 460 so she will not be admitted. D) The top 30% is defined with a score greater than or equal to 431.4 so she will not be admitted.

Question

Mathematics

Buchanan

7 December, 06:25

Admission to a certain university is determined by an entry exam. The scores of this test are Normally distributed with a mean of 400 and a standard deviation of 60. Only students who score in the top 30% will be offered admission. Amy scores 425 on the test. Choose the most accurate statement? A) The top 30% is defined with a score less than or equal to 431.4 so she will be admitted. B) The top 30% of all students have scores greater than or equal to 520 so she will not be admitted. C) The top 30% of all students have scores greater than or equal to 460 so she will not be admitted. D) The top 30% is defined with a score greater than or equal to 431.4 so she will not be admitted.

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Nicholas Bright · Answer 1

The top 30% is defined with a score greater than or equal to 431.44 so she will not be admitted (D)

Step-by-step explanation:

Mean m = 400

Standard deviation S = 60

Firstly, we have to determine the cut off mark,

Since Only students who score in the top 30% are accepted, the cut off mark can be determined from 70% of the mark.

P (cut off mark = X) = Z[ (X - m) / S)
=¢ (X-400/60) = 0.7

From Normal distribution table,

X-400/60 = 0.524

X = 431.44

Therefore, the cut off mark is 431.44

Since Amy scores 425 on the test.

Therefore, The top 30% is defined with a score greater than or equal to 431.44 so she will not be admitted (D)