In: Math

**A data set includes 103 body temperatures of healthy
adult humans having a mean of 98.5°F and a standard deviation of
0.61°F. Construct a 99% confidence interval estimate of the mean
body temperature of all healthy humans. What does the sample
suggest about the use of 98.6°F as the mean body
temperature?**

**What is the confidence interval estimate of the
population mean μ?**

**°F < μ < °F**

**(Round to three decimal places as
needed.)**

Solution :

Given that,

sample mean =
= 98.5

Population standard deviation =
=0.61

Sample size = n =103

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_{/2}
= Z_{0.005} = 2.576

Margin of error = E = Z_{/2}*
(
/n)

= 2.576* ( 0.61/ 103)

= 0.155

At 99% confidence interval estimate of the population mean is,

- E < < + E

98.5-0.155 < < 98.5+0.155

**°F**98.345<
<98.655 **°F**

(, )

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