A national air traffic control system handled an average of 47,795 flights during 30 randomly selected days in a recent year. The standard deviation for this sample is 6,371 flights per day. Complete parts a through c below.

a). Construct a 99% confidence interval to estimate the average number of flights per day handled by the system.

b.) Suppose the current system can safely handle 50,000 flights per day. What conclusions can be drawn with these results?
A. Since the 99% confidence interval does not contain 50,000, it can be said with 99% confidence that 50,000 flights per day can be safely handled. B. Since the 99% confidence interval contains 50,000, it can be said with 99% confidence that 50,000 flights per day can be safely handled. C. Since the 99% confidence interval contains 50,000, it cannot be said with 99% confidence that 50,000 flights per day can be safely handled. D. Since the 99% confidence interval does not contain 50,000, it cannot be said with 99% confidence that 50,000 flights per day can be safely handled.

c). What assumptions need to be made about this population?
A. Since the sample size is not larger than 30, one needs to assume that the population follows the Student's t-distribution. B. Since the sample size is not larger than 30, one needs to assume that the population distribution is not very skewed to one side. C. Since the sample size is not larger than 30, one needs to assume that the population distribution is skewed to one side. D. Since the sample size is not larger than 30, one needs to assume that the population follows the normal probability distribution.