Lance P. answered • 10/07/19
SWAG--UM (Students Will Achieve Greatness & Understanding in Math)
What percentage of a temperatures lies within 2 standard deviations of the mean ?
The mean temperature was 64.2 degrees with a standard deviation of 3.1 degrees.
Since the mean is 64.2 degrees adding 3.1 degrees twice to the right and subtracting 3.1 degrees twice from the left will yield us the range of temperatures within two standard deviations of the mean on the bell curve.
64.2 + 3.1 + 3.1 = 70.4
64.2 - 3.1 - 3.1 = 58
We can apply the 68/95/99 rule and its derivations to answer the question. In certain textbooks, the percentage of values that is 1 standard deviation to the right of the mean is roughly 34.13%, so using the mean as a line of symmetry, the percentage of values 1 standard deviation to the left is also 34.13%.
To find the percentage of values that lie within (between) 1 standard of the mean (both left and right) is 34.13 * 2 = 68.26% ∼68%
The percentage of values situated between one and two standard deviations to the right is 13.59% which is the same percentage for the left. Thus to find the percentage of values within 2 standard deviations of the mean is:
Sum of two standard deviations (SD) to the right = % of 1 SD + % between 1 and 2 SD
Sum of two SDs to the left = % of 1 SD + % between 1 and 2 SD
Left
34.13% + 13.59 = 47.72%
Right
34.13 + 13.59 = 47.72%
Total Percentage = Left + Right = 95.44% ∼ 95%
***Note*** You could find only one side of the bell curve and multiply by 2 to derive an efficient and quicker calculation.
