Question

(AKS 24): 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?

Answer 1

Explanation:

Let x be the random variable representing the set of art exam scores. Since they are normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 81

σ = 10

the probability of getting a score lower than 78 is expressed as

P(x < 78)

For x = 78,

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

Looking at the normal distribution table, the probability corresponding to the z score is 0.38

Therefore, the percentage of exam scores that are lower than Calvin's score is

0.38 × 100 = 38%