Question

Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?

Answer 1

Let X be the normal random variable denoting the scores of the students. Given that mean µ = 500 and s.d σ = 100. The total area under the normal curve represents the total number of students who took the test. If we multiply the values of the areas under the curve by 100, we obtain percentages.

When X = 585, Z = (585 - 500)/100 = 0.85 

The proportion of students who scored below 585 is given by P[area to the left of Z = 0.85] 

(i.e.) P (Z < 0.85) = 0.5 + P (0 < Z < 0.85) 

= 0.5 + 0.3023 . 

= 0.8023 

= 80.23% 

Raghul scored better than 80.23% of the students who took the test and he will be admitted to this university.