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.

Answer 2

68 percent of the scores would fall between 85 and 115.

Empirical rule

Empirical rule states that for a normal distribution, about 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.

Given that mean(μ) = 100 and standard deviation (σ) = 15

68 percent of the scores would fall between μ ± σ = 100 ± 15 = 85, 115

68 percent of the scores would fall between 85 and 115.

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