Real-Life Scenarios
Text Version

(Introduction music)
Image description: Andrew, Khalid and Justyce are sitting together at a table in math class. Documents and calculators are on the table.

Andrew: How are those percentages different from the 68-95-99.7 percentages?

Justyce: Look at the normal curve with those percentages.

Image description: A graph of the normal curve appears on screen:
The horizontal axis is labeled ‘standard deviations’ and extends from negative infinity to infinity (not shown), counting in increments of one. There is no vertical axis shown The curve starts just above where  negative 4 would be, rises to a maximum point when x = 0, and then decreases to just above where 4 would be. The area under the curve is divided into eight sections. The first section extends from negative infinity to negative 3, and is labeled 0.13%. The second section extends from negative 3 to negative 2, and is labeled 2.15%. The third section extends from negative 2 to negative 1, and is labeled 13.59%. The fourth section extends from negative 1 to 0, and is labeled 34.13%. The fifth section extends from 0 to 1, and is labeled 34.13%. The sixth section extends from 1 to 2, and is labeled 13.59%. The seventh section extends from 2 to 3, and is labeled 2.15%. The eighth section extends from 3 to infinity and is labeled .13%. Above the curve, different sections of the area under the curve are detailed. The section that extends from negative 1 to 1 is labeled 68.26%. The section that extends from negative 2 to 2 is labeled 95.44%. The section that extends from negative 3 to 3 is labeled 99.74%

Justyce: Those percentages talk about a range of values. For example, you can talk about the presidents who fell between one standard deviation from the mean.

Image description: Justyce points and slides her finger from  plus 1 to negative 1 on the graph.

Justyce: One standard deviation from the mean for the presidents was about 48 years to 61 years. That would be the 68.26%.

Image description: Justyce points to 68.26% on the graph.

Justyce: These percentages can only be discussed with respect to the mean and standard deviation.

Khalid: The other percentage was just for one age, not a range. And it did not have to be a certain standard deviation from the mean.