Question

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.)

Answer 1

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

°F98.345< <98.655 °F

(, )