Question

most people think that the
ormal\ adult body temperature is 98.6°f. in a more recent study, researchers reported that a more accurate figure may be 98.3°f. furthermore, the standard deviation appeared to be around 0.7°f. assume that a normal model is appropriate. complete parts a through c below.
a) in what interval would you expect most peoples body temperatures to be? explain. select the correct choice below and fill in the answer box(es) to complete your choice.
○ a. using the 68 - 95 - 99.7 rule, about 95% of the body temperatures are expected to be less than □°f
(round to one decimal place as needed.)
○ b. using the 68 - 95 - 99.7 rule, about 95% of the body temperatures are expected to be at least □°f
(round to one decimal place as needed.)
○ c. using the 68 - 95 - 99.7 rule, about 95% of the body temperatures are expected to be between □°f and □°f
(use ascending order. round to one decimal place as needed.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule for a normal distribution states that about 95% of the data lies within 2 standard deviations of the mean.

Step2: Calculate the lower and upper bounds

Given the mean \(\mu = 98.3^{\circ}F\) and standard deviation \(\sigma=0.7^{\circ}F\).
The lower bound is \(\mu - 2\sigma=98.3-2\times0.7\).

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The upper bound is \(\mu + 2\sigma=98.3 + 2\times0.7\).

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Answer:

C. Using the 68 - 95 - 99.7 Rule, about 95% of the body temperatures are expected to be between \(96.9^{\circ}F\) and \(99.7^{\circ}F\)