For a bell-shaped data set, approximately what percentage of the data will be in the interval $\mu -\sigma$ to $\mu +\sigma$?

• A. About 99.7%
• B. About 50%
• C. About 68%
• D. About 95%

Answer: (C)

Verified step by step guidance

1. Recognize that the problem refers to a bell-shaped data set, which typically implies a normal distribution characterized by its mean (\$\mu\$) and standard deviation (\$\sigma\$).
2. Recall the Empirical Rule (or 68-95-99.7 rule), which describes the percentage of data within certain intervals around the mean in a normal distribution.
3. According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, i.e., in the interval \$\mu - \sigma\$ to \$\mu + \sigma\$.
4. Understand that the other percentages given (about 95% and about 99.7%) correspond to intervals of two and three standard deviations from the mean, respectively.
5. Therefore, the interval \$\mu - \sigma\$ to \$\mu + \sigma\$ contains about 68% of the data in a normal distribution.