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

98.3198.31degrees°F

and a standard deviation of

0.420.42degrees°F.

Using the empirical rule, find each approximate percentage below.

a.

3

deviationsdeviations

97.0597.05degrees°F

99.5799.57degrees°F?

b.

97.8997.89degrees°F

98.7398.73degrees°F?

a. Approximately

99.799.7 %

of healthy adults in this group have body temperatures within

3

standard

deviationsdeviations

of the mean, or between

97.0597.05degrees°F

and

99.5799.57degrees°F.

(Type an integer or a decimal. Do not round.)

b. Approximately

what %

of healthy adults in this group have body temperatures between

97.8997.89degrees°F

and

98.7398.73degrees°F.

please explain everything in detail; and please anwer this if you r sure you know it.

thank you

a.

What is the approximate percentage of healthy adults with body temperatures within

3

standard

deviationsdeviations

of the mean, or between

97.0597.05degrees°F

and

99.5799.57degrees°F?

b.

What is the approximate percentage of healthy adults with body temperatures between

97.8997.89degrees°F

and

98.7398.73degrees°F?

Explanation / Answer

In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations.

a) 99.7%

b) 98.31 - 0.42 = 97.89

Within 1 standard deviation

68.3%

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