Question

Suppose that scores of the entrance test of UMAC are normally distributed with mean 500 and standard deviation 100. A class of 25 candidates, was invigilated by me last weekend for the entrance of UMAC 2021. Suppose that candidates in my class are randomly assigned, find the probability that the average score of that class will be no more than 535.

Answer 1

Here Mean = = 500

standard deviation = = 100

sample size =n = 25

standard error = /sqrt(n) = 100/sqrt(25) = 20

P( 535) = NORMAL( 535; 500; 20)

Z = (535 - 500)/20 = 1.75

P( 535) = NORMAL( 535; 500; 20)

= NORMSDIST(1.75)

P( 535) = 0.96