Question

Which of the following is true about the Empirical Rule?

a. 68% of the observations lie between – 2 and + 2 standard deviations from the mean.
b. 95% of the observations lie between – 3 and + 3 standard deviations from the mean.
c. 99.7% of the observations lie between – 1 and + 1 standard deviations from the mean.
d. 95% of the observations lie between – 2 and + 2 standard deviations from the mean.
e. 68% of the observations lie between – 3 and +3 standard deviations from the mean.

Answer 1

The correct statement about the Empirical Rule is that 95% of the observations lie between – 2 and + 2 standard deviations from the mean.

Step-by-step explanation:

The Empirical Rule is an important concept in statistics associated with normally distributed data. When data has a bell-shaped distribution, the rule states the following percentages of observations within standard deviations from the mean:

• About 68 percent of the observations lie within one standard deviation of the mean (±1σ).
• About 95 percent of the observations lie within two standard deviations of the mean (±2σ).
• About 99.7 percent of the observations lie within three standard deviations of the mean (±3σ).

Using these facts, the correct answer to the question Which of the following is true about the Empirical Rule? is d. 95% of the observations lie between – 2 and + 2 standard deviations from the mean.