Question

Scores on a recent national statistics exam were normally distributed with a mean of 88 and a standard deviation of 2.

1. What is the probability that a randomly selected exam will have a score of at least 85?

2. What percentage of exams will have scores between 89 and 92?

3. If the top 5% of test scores receive merit awards, what is the lowest score eligible for an award?

I do not understand how to compute probability.

Answer 1

Use R software to compute all of these.

1. Use code pnorm(85,88,2,lower.tail = F)
The answer is 0.9331928.

2. Use code pnorm(92,88,2) - pnorm(89,88,2)

The answer is 0.2857874 i.e. 28.6%.

3. Use the code qnorm(0.05,88,2,lower.tail = F)

The answer is 91.28971.