The body temperatures of a group of healthy adults have a bell-shaped distributi

Question

The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.37degreesF and a standard deviation of 0.69degreesF. Using the empirical rule, find each approximate percentage below.

a. What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between 97.68degreesF and 99.06degreesF?

b. What is the approximate percentage of healthy adults with body temperatures between 96.99degreesF and 99.75degreesF?

Explanation / Answer

Sol:

mean=98.37

sd=0.69

P(97.68<X,99.06)

P(97.68-98.37/0.69<Z<99.06-98.37/0.69)

P(-1<z<1)

=0.6826

the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between 97.68degreesF and 99.06degreesF is 0.6826*100=68.26%

Solutionb:

P(96.99<X<99.75)

P(96.99-98.37/0.69<Z<99.75-98.37/0.69)

P(-2<Z<2)

=0.9544

=0.9544*100=95.44%

is the approximate percentage of healthy adults with body temperatures between 96.99degreesF and 99.75degreesF is 95.44%

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