Question

In a set of normally distributed test scores that have a mean of 100 and standard deviation of 15, it would be correct to conclude that approximately 68 percent of the scores would fall between _____ and _____.

Answer 1

Answer:

It would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.          

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution is a bell shaped distribution that is a normal distribution.

Empirical rule

• Also known as 68-95-99.7 rule.

• It states that almost all data lies within three standard deviation of mean for a normal distribution.
• About 68% of data lies within one standard deviation of mean.

• About 95% of data lies within two standard deviation of mean.

• About 99.7% of data lies within three standard deviation of mean.

Thus, approximately 68% of data will lie within one standard deviation of mean.

$\mu - \sigma = 100-15 = 85\\\mu + \sigma = 100 + 15 = 115$

Thus, it would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.