We are trying to estimate how long it takes to prepare a school lunch. In a test kitchen, a sample of 100 school lunches was prepared. The average time per lunch was 10 minutes.

Assume that we know the population standard deviation (sigma) and that it is 3 minutes.

(This allows us to use the Z-distribution, instead of t).

a) Find the lower confidence limit and upper confidence limit for a 95% confidence interval.

In this problem, instead of using 1.96, for convenience we will round off the Z corresponding to the 95% confidence level to 2. This will give us a slightly wider interval.

b) As a bonus question, return to the Jake’s Cakes example in the chapter and see what the confidence intervals look like as you vary the given information – the sample mean time, the sample variability, and the sample size.