The 95% confidence interval for the mean is 14.88−15.12 hours.
The correct answer between all the choices given is the second choice or letter B. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.
We are given the following data:
Sample Size = n = 1000
Sample Mean = u = 15 hours
Population Standard Deviation = s = 2 hours
Since we know the population standard deviation, we can use z distribution to find the confidence interval about the mean. z value for 95% confidence interval is 1.96.
Formula for the confidence interval is:
[tex] (u-z\frac{s}{\sqrt{n}} , u+z\frac{s}{\sqrt{n}}) [/tex]
Using the values in the formula, we get:
[tex] (15-1.96\cdot\frac{2}{\sqrt{1000}}, 15+1.96\cdot\frac{2}{\sqrt{1000}})\\ \\
(14.88,15.12) [/tex]
Therefore, the 95% confidence interval about the population mean is 14.88 hours to 15.12 hours. So B option is the correct answer.
