Question

Which of the following values best represents the proportion of data within 2 standard deviations in a normal distribution?

• A. 0.90
• B. 0.68
• C. 0.95
• D. 0.93

Hint:

Remember the 68–95–99.7 rule: 1$\sigma$ → 68% \quad 2$\sigma$ → 95% \quad 3$\sigma$ → 99.7%.

Answer 1

The Correct Option is C

Step 1: Recall the Empirical Rule.
In a normal distribution, the Empirical Rule (also called the 68–95–99.7 rule) describes how data is distributed around the meanThis rule states that approximately 68% of the data lies within 1 standard deviation of the mean
Step 2: Apply the rule for 2 standard deviations.
According to the same rule, approximately 95% of the data lies within 2 standard deviations of the meanThat means the probability that a value falls between $\mu - 2\sigma$ and $\mu + 2\sigma$ is about 0.95
Step 3: Compare with given options.
0.68 corresponds to 1 standard deviation
0.95 corresponds to 2 standard deviations
0.997 corresponds to 3 standard deviations (not given)
Step 4: Conclusion.
Therefore, the value that best represents the proportion of data within 2 standard deviations in a normal distribution is 0.95