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:
\((u-z\frac{s}{\sqrt{n}} , u+z\frac{s}{\sqrt{n}})\)
Using the values in the formula, we get:
\((15-1.96\cdot\frac{2}{\sqrt{1000}}, 15+1.96\cdot\frac{2}{\sqrt{1000}})\\ \\
(14.88,15.12)\)
Therefore, the 95% confidence interval about the population mean is 14.88 hours to 15.12 hours. So B option is the correct answer.
