Question

A set of art exam scores are normally distributed with a mean of

81 points and a standard deviation of 10 points. Calvin got a score of 78 on
the exam.
What percentage of exam scores are lower than Calvin's score?
a) 61.79%
b) 65.17%
c) 34.83%
d) 38.21%

Answer 1

The percentage of people that scored less than Calvin is 38.21 %

Explanation:

In this question, we are concerned with calculating the percentage of exam scores lesser than what Calvin scores.

To calculate this, we first need to calculate the standard score or the z-score of Calvin result.

Mathematically;

z = (x - mean)/SD

from the question, x = 78, mean = 81 and SD = 10

Substituting this, we have

z = (78 -81)/10 = -3/10 = -0.3

So we proceed to calculate the probability.

P(x < 78) or P(z < -0.3)

We make use of the standard table to get this probability

P(z< - 0.3) = 0.38209

In percentage, this is same as 38.209% or more simply 38.21%