Stat 1: Practice Normal Computations with Body Temperature
Suppose that the body temperatures of healthy adults vary from person to person according to
a Normal distribution with mean µ = 36.8 and standard deviation σ = 0.4 degrees Celsius. For
brevity we can write
1) Between about what two values do the middle 68% of Celsius body temperatures fall?
Using the 68/95/99.7 rule, we know that about 68% of people have body temperatures within
±1 standard deviation of the mean, so between 36.8−0.4 = 36.4 degrees and 36.8+0.4 = 37.2
degrees Celsius.
2) Between about what two values do the middle 95% of Celsius body temperatures fall?
Again using the 68/95/99.7 rule, we know that about 95% of people have body temperatures
within ±2 standard deviation of the mean, so between 36.8 − 2(0.4) = 36.0 degrees and
36.8 + 2(0.4) = 37.6 degrees Celsius.
3) About what percent of body temperatures are above 37.6 degrees Celsius?
37.6 is 2 standard deviations above the mean. We know that about 95% of people have
temperatures within ±2 sd’s of the mean, so that leaves a total of about 5% with values more
extreme than this (in either direction). The symmetry of the Normal distribution implies
that half of these, or about 2.5% of all people have values more than 2 sd’s above the mean
or above 37.6 degrees (and about 2.5% have values less than 2 sd’s below the mean, or below
36.0 degrees).
4) About what percent are between 36.4 and 37.6 degrees Celsius?
37.6 is two standard deviations above the mean, so only about 2.5% of people have tempera-
tures higher than this and 97.5% have values less than or equal to 37.6. 36.4 is one standard
deviation below the mean, so about 16% (half of the 32% that are not within ±1 standard
deviations of the mean) are below this value. That means that about 97.5% − 16% = 81.5%
of people have temperatures between 36.4 and 37.6 degrees Celsius.
5) Above about what value are the highest 16% of body temperatures?
About 32% of people have temperatures more than one standard deviation from the mean
and, due to the symmetry of the distribution, half of these people, or 16% of all people have
temperature more than one standard deviation above the mean, or 36.8+0.4 = 37.2 degrees.