Question

The scores on an admission test are normally distributed with a mean of 640 and a standard deviation of 105.7. A student wants to be admitted to this university. He takes the test and scores 755. What is the probability of him to be admitted to this university?

(a) 65.9%

(b) 84.6%

(c) 40.9%

(d) 54%.

This question was addressed to me in quiz.

My question comes from Probability Distribution topic in portion Discrete Probability of Discrete Mathematics

Answer 1

Correct option is (b) 84.6%

Explanation: Let k be the random variable that represents the scores. k is normally distributed with a mean of 640 and a standard deviation of 124.7. The total area under the normal curve represents the total number of students who take the test. If we multiply the values of the areas under the curve by 124.7, we obtain percentages. Now, for k = 755, z = \(\frac{755 – 640}{105.7}\) = 1.087. The proportion of the students who scored below 755 is given by, P = [area to the left of z = 1.087] = 0.846. Hence, the required probability is 84.6 %.