Question

The grades on the last math exam had a mean of 72%. Assume the population of grades on math exams is known to be distributed normally, with a standard deviation of 5%. Approximately what percent of students earn a score between 72% and 87%? 49.9% 1% 50% 47.7%

Answer 1

Answer:

0.4987, so 49.9%

Step-by-step explanation:

We will need to find 2 z-scores for this situation.  We are asked to find the probability of scores between 72% and 87%.  

We are given:

µ = 72%

σ = 5%

x = 72% - 87%

So we need:

P(72 < x < 87)

Find the z-score for 72:

z = (72 - 72)/5 = 0

Find the z-score for 87:

z = (87 - 72)/5 = 3

So we have

P(72 < x < 87) = P(0 < z < 3) = P(z < 3) - P(z < 0)

P(z < 3) = 0.9987

P(z < 0) = 0.500

So we have

0.9987 - 0.500 = 0.4987