Answer:
Step-by-step explanation:
We want to determine a 99% confidence interval for the mean amount of time that students spend in the shower each day.
Number of sample, n = 12
Mean, u = 4.75 minutes
Standard deviation, s = 1.26 minutes
For a confidence level of 99%, the corresponding z value is 2.58. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean ± z ×standard deviation/√n
It becomes
4.75 ± 2.58 × 1.26/√12
= 4.75 ± 2.58 × 0.364
= 4.75 ± 0.939
The lower end of the confidence interval is 4.75 - 0.939 = 3.811
The upper end of the confidence interval is 4.75 + 0.939 =5.689
Therefore, with 99% confidence interval, the mean amount of time that students spend in the shower each day is between 3.811 minutes and 5.689 minutes
