Given a population of 5000 scores with a mean of 86 and a standard deviation of 10, how many scores are between 76 and 86?

Question

Given a population of 5000 scores with a mean of 86 and a standard deviation of 10, how many scores are between 76 and 86?

Answer 1

Find need to find the probability that a score is between 76 and 86

Let x be a score want to find P(76 < x < 86) where x is N(86,10)

Transform limits 76 and 86 to N(0,1) using transformation

z = (x - mean)/SD = (x - 86)/10

For x = 76, z = -1

For x = 86, z = 0

P(76 < x < 86) = P(-1 < z < 0) = P(z < 0) - P(z < -1) = 0.5 - 0.1587 = 0.3413

So out of 5000 people, 5000 * 0.3413 = 1706.f ~ 1707 will have score between 76 and 86