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S. (10 pts) A manufacturer has developed a new gun powder and he would like to estimate the average muzzle velocity with his new powder. The gun smith collected a random sample of 20 shells and found the average muzzle velocity to be a? = 2959 feet per second. Assume muzzle velocities are normally distributed with a standard deviation of o = 40 feet per second. a) Find the margin of error for a 98% condence interval for the true mean muzzle velocity in shells using the new gun powder. (3) b) Find a 98% condence interval for the true mean muzzle velocity in shells using the new gun powder. (3) c) A consumer report for gun enthusiasts reports that the average muzzle velocity for these types of shells is 2921 feet per second. Can the gun manufacturer claim that his new gun powder will produce a higher average velocity in these shells based on the result from part (b)? (2 pts) i. Yes because 2921 feet per second is obviously below 2959 feet per second. ii. No because 2921 feet per second 1s still a possible value for the true average muzzle velocity of the new gun power, because values below 2921 feet per second are included in the CI from part (b). iii. Yes because no values below 2921 feet per second are included in the CI from part (b). iv. No because 2921 is within 40 of 2959 cl) Suppose the manufacturer collected muzzle velocities from 36 shells. Find the margin of error for a 98% condence interval for the true mean muzzle velocity in shells using the new gun powder. (2)