Question

11 what is the approximate area under the entire curve?
12 what percent of the area under the curve is between 1 standard deviation above and below the mean?
13 what percent of the area under the curve is between 2 standard deviations above and below the mean?

Explanation:

These questions refer to the standard normal distribution curve, a fundamental concept in statistics. For this curve:

1. The total area under the entire curve represents the total probability of all possible outcomes, which is defined as 1 (or 100% when expressed as a percentage).
2. The empirical rule (68-95-99.7 rule) for normal distributions states that ~68% of data falls within 1 standard deviation of the mean.
3. The same empirical rule states that ~95% of data falls within 2 standard deviations of the mean.

Answer:

1. 1 (or 100%)
2. 68%
3. 95%