Answer:
Confidence interval for the true mean number of reproductions per hour for the bacteria is (10.1,10.5).
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 10.3
Population standard deviation, σ = 2.1
Sample size, n = 728
Alpha, α = 0.01
Confidence interval:
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58[/tex]
[tex]10.3 \pm 2.58(\frac{2.1}{\sqrt{728}} ) = 10.3 \pm 0.2008 = (10.0992,10.5008) \approx (10.1,10.5)[/tex]
