(12 pt) A cola company wants to estimate the mean amount of cola in the 16-ounce bottles it produces. a. (3) If a simple random sample of 50 bottles is taken, nd the probability that the difference between the sample mean and population mean will not exceed 0.01 ounce. For this part, let's assume that the population standard deviation for the amount of cola in all the 16-ounce bottles the company produces is 0' = 0.05 ounce. b. (3) Suppose out of a random sample of 50 bottles of cola, the sample mean is 15.97 ounces and the sample standard deviation is 0.04 ounces. Find a one-sided 98% condence interval with a lower bound for the true mean amount of cola of all the 16-ounce bottles the company produces. c. (2) Interpret the condence interval that you obtained in part (b). d. (3) With the help of the sample information from part (b), how many bottles should the company sample so that the probability will be 0.99 that the sample mean will be within 0.02 ounce of the true population mean? 6. (1) Can you justify the solutions you've derived in parts (a), (b) and ((1)? Explain