Question

Scores on a recent national statistics exam were normally distributed with a mean of 82 and a standard deviation of 4.

1. What is the probability that a randomly selected exam will have a score of at least 87?
2. What percentage of exams will have scores between 80 and 85?
3. If the top 3% of test scores receive merit awards, what is the lowest score eligible for an award?

Answer 1

Given that, mean = 82

stsndard deviation = 4

i) We want to find, P(X >= 87)

Therefore, required probability is 0.1056

ii) We want to find, P(80 < X < 85)

Therefore, required probability is 0.4649

iii) We want to find, the value of x such that, P(X > x) = 0.03

Therefore, lowest score eligible for an award is 89.52