The 68-95-99.7 Rule

Question

Consider that the National Health Center for Statistics reports that females (age 21) have heights that are normally distributed, approximately centered at a mean of 65 inches (5 feet 5 inches) with a standard deviation of 2.5 inches. Use the 68-95-99.7 Rule to find the percentage of females (age 21) with heights in each of the following scenarios:

3. Percentage of heights greater than 67.5:
%

4. Percentage of heights less than 70:
%

5. Percentage of heights between 62.5 and 65:
%

6. Percentage of heights between 62.5 and 70:
%

Answer 1

3. Percentage of heights greater than 67.5: 16%

4. Percentage of heights less than 70:         2.5%

5. Percentage of heights between 62.5 and 65: 34%

6. Percentage of heights between 62.5 and 70: 81.5%

 

How to do this, on paper, with the given rule stated:

Draw a normal curve, and put a vertical line at the mean, labeled on the x-axis as 65" (mean)

Draw two vertical lines through the curve, to the right of the vertical mean line labeling the x-values 67.5" and 70", respectively.  In the area under the curve, label the region between x=65 & x=67.5  as 34% and the next region to the right as 13.5%.

 

To the left of the vertical mean line, make two more vertical lines, identified by x=62.5" and (further left) x=60".

The area under the curve between the mean and x=62.5 is labeled as 34% and the area just to its left is labeled 13.5%.

 

 Use this to add up all the appropriate areas in these questions.