A normally distributed set of scores has a μ = 58 and a σ = 6. What is the probability that a randomly selected score will fall between 55 and 61?
A) .3413
B) .6170
C) .3830
D) .5000

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected score will fall between 55 and 61, we need to find the area under the normal curve between those two scores. First, we need to convert these scores to z-scores:
z1 = (55 - 58) / 6 = -0.50
z2 = (61 - 58) / 6 = 0.50
Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:
P(z < -0.50) = 0.3085
P(z < 0.50) = 0.6915
To find the probability between these two z-scores, we subtract the smaller probability from the larger probability:
P(-0.50 < z < 0.50) = P(z < 0.50) - P(z < -0.50) = 0.6915 - 0.3085 = 0.3830
So the probability that a randomly selected score will fall between 55 and 61 is 0.3830 or 38.3%. Therefore, the correct choice is C.

A Normally Distributed Set of Scores Has a μ =