Kindly provide the step by step solution in manual calculation (no internet and website )

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.6 days. Assume the population standard deviation is known to be 5.6 days. Answer the following questions:

1. What is the cut-off point at alpha = .05?

2. What is the cut-off point if Type I error is 1%?

3. Would you reject the Null at 5% level of significance?

4. Would you reject the Null at 1% level of significance?

5. If suppose the true delivery time for the population is 17 days. What is the Type II error at Alpha = .01?

6. If suppose the true delivery time for the population is 17 days. What is the Type II error at Alpha = .05?