Answer:
The 85% confidence interval is ( 7.7 , 8.0 )
Step-by-step explanation:
In order to find the 85% confidence interval you use the following formula:
[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
where
[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8
σ: standard deviation = 2.2
n: sample size = 967
α: 1 - 0.85 = 0.15
Zα/2: Z factor of the density distribution = 1.44
You replace the values of all parameters in the equation (1):
[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]
Then, the confidence interval is:
[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]
