4. A processor of carrots cuts the green top off each carrot, washes the carrots, and insertssix to a package. Twenty packages are inserted in a box for shipment. To test the weightof the boxes, a few are sampled. A sample of 16 boxes revealed a mean weight of 20.5 pounds. The population standard deviation is 0.51 pound.

a. Develop a 95% confidence interval for the mean weight of the boxes. Report the margin of error.

b. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pound (E = 0.2)?

c. Repeat part a using the sample size you found in part b. Report the margin of error.