Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 200 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.7 seats and the sample standard deviation is 4.2 seats. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) (i) Enter an exact number as an integer, fraction, or decimal. X = (ii) Enter an exact number as an integer, fraction, or decimal. SX = (ii) Enter an exact number as an integer, fraction, or decimal n= (iv) Enter an exact number as an integer, fraction, or decimal. n - 1= Part (b) In words, define the random variables X and X. O X is the number of un pied seats on a flight, and X is the average number of occupied seats for a sample of 200 flights. O X is the number of un seats on a flight, and X is the average number of unoccupied seats for a sample of 200 flights. O X is the number of full flights, and X is the average number of full flights for a sample of 200 flights. O X is the number of full flights, and X is the average number of full flights for a sample of 200 flights. Part (c) Which distribution should you use for this problem? (Enter your answer in the form z or tay where df is the degrees of freedom.) Explain your choice. O The standard normal distribution should be used because the sample size is very large. The Student's t-distribution should be used because the population standard deviation is not given. The standard normal distribution sample standard deviation is known. The normal distribution should be used because we are interested in proportions and the sample size is large. Part (d) Construct a 92% confidence interval for the population mean number of unoccupied seats per flight. (i) State the confidence interval. (Round your answers to two decimal places.) ii) Sketch the graph. C.L. = - =L X (iii) Calculate the error bound. (Round your answer to two decimal places.)A quality control specialist for a restaurant chain takes a random sample of size 15 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.50 with a sample standard deviation of 1.59. Assume the underlying population is normally distributed. We wish to construct a 95% confidence interval for the true population mean for the amount of soda served. What is the error bound? (Round your answer to two decimal places.)