(Solved): Wayne Musickal is a renowned manufacturer of handmade pianos. The handmade piano is time-consuming, ...

Wayne Musickal is a renowned manufacturer of handmade pianos. The handmade piano is time-consuming, and Wayne Musickal wants to conduct a test to have improved knowledge of the manufacturing time.  Considering 40 pianos that are randomly selected as a sample for observation, the average manufacturing time was 654.16 minutes, and the standard deviation was 164.43.

1. (2 points) Calculate a 95% two-sided confidence interval for the true average manufacturing time of all handmade pianos from which the sample was selected
2. (2 points) Determine 95% confidence interval for the population standard deviation of the manufacturing time.
3. (2 points) Suppose Wayne Musickal had made a rough guess that the standard deviation is 160 minutes before collecting the data, and expected that their error will be at most 40 minutes. What sample size should be used at a confidence level of 95%?