5. What percentage of the scores are within one standard deviation of the mean ?

*
Hint: Divide the number of items in the list from problem #4 by the total number of test scores, and then multiply by 100 to convert the decimal into percent.
A. 65%
B. 70%
C. 75%
D. 80%

1 answer

To determine the percentage of scores that are within one standard deviation of the mean, you typically use the empirical rule (also known as the 68-95-99.7 rule) in a normal distribution. According to this rule:

  • Approximately 68% of the data falls within one standard deviation of the mean.

However, since you provided a hint that involves specific numbers from a previous problem (problem #4) and that you need to perform a calculation based on those results, you would need that specific data to accurately calculate the percentage.

If you already have the number of scores that fall within one standard deviation (let's call it "N_within_1_sd") and the total number of scores (let's call it "N_total"), you can calculate the percentage as follows:

\[ \text{Percentage} = \left( \frac{N_{\text{within 1 sd}}}{N_{\text{total}}} \right) \times 100 \]

Without the specific values from problem #4, I cannot give you the exact percentage. However, based on the empirical rule, if the distribution of scores is approximately normal, you could consider that about 68% of the scores would fall within one standard deviation of the mean.

Thus, if you were to select an option based on general statistical knowledge, you might choose:

A. 65%

But again, to accurately answer your question, you would need the specific data from problem #4 to perform the calculation.