Question

If a particular set of data is approximately normally distributed, we would find that approximately

A) 2 of every 3 observations would fall between ±1 standard deviation around the mean.
B) 4 of every 5 observations would fall between ±28 standard deviations around the mean.
C) 19 of every 20 observations would fall between ±2 standard deviations around the mean.
D) all the above

Answer 1

Option A) 2 of every 3 observations would fall between ±1 standard deviation around the mean.

Step-by-step explanation:

The correct answer is A) 2 of every 3 observations would fall between ±1 standard deviation around the mean. This is known as the Empirical Rule for a bell-shaped and symmetric distribution.

According to the Empirical Rule, approximately 68 percent of the data falls within one standard deviation of the mean, approximately 95 percent falls within two standard deviations, and more than 99 percent falls within three standard deviations.

Therefore, option A) is the most accurate description of the distribution of data that is approximately normally distributed.