Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25.Using this information,what percentage of the population scores between 10 and 20?
A)53.28%
B)59.87%
C)49.13%
D)50.00%
E)68.26%

Question

Quizplus · Accepted Answer

To find the percentage of the population that scores between 10 and 20, we use the properties of the normal distribution. The mean (μ) is 15, and the standard deviation (σ) is the square root of the variance, which is √25 = 5. We convert the scores 10 and 20 into z-scores: z = (X - μ) / σ. For X = 10, z = (10 - 15) / 5 = -1. For X = 20, z = (20 - 15) / 5 = 1. The percentage of the population between z = -1 and z = 1 in a standard normal distribution is approximately 68.26%.

Suppose the Distribution of Integrity Test Scores Is Normally Distributed