The Food and Drug Administration (FDA) oversees the approval of both medical devices and new drugs. To gain FDA approval, a new device must be shown to perform at least as well, and hopefully better, than any similar device already on the market. Suppose a medical device company develops a new system for connecting ntravenous tubes used on hospital patients. To be comparable to an already-existing product, the force required o disconnect two tubes joined by the new device must not exceed 5 lb. To estimate the maximum force required to disconnect two tubes, several tests are made. For a random sample of n connections, the forces X₁, X2, X3, . .., <ʼn required to disconnect the tubes are recorded and the maximum, M, of the n readings is used to estimate the maximum necessary force for all such connections. Suppose that the actual distribution of forces needed to disconnect tubes can be described by a uniform distribution on the interval [2, 4]. For a sample of size n = 2, do you expect the mean of the sampling distribution of M to be closer to 2 or 4?

are F2 and F3 conservative? also what about parts B and C?

Imagine a diver jumping off a spring board that is 10 feet above the water. The board throws the diver up with an upward velocity of 9 feet per second. That means that if there were no gravity, the diver would keep going up at the rate of 9 feet every second. Fortunately for the diver, there is gravity. Eventually, gravity over comes the force of the diving board and the the diver begins to come down. So over all, the diver is thrown into the air fairly quickly, he slows down until he stops, then begins to come back down (slowly at first, then faster and faster until he hits the water). The height of any object like the diver that is projected into the air can be modeled with the following function: h(t) = -16t^2 + v*t + m In this function: h(t) is the height of the object t seconds after it was thrown into the air. t is the number of seconds after the object was thrown in the air. v is the initial upward velocity (for the diver this was 9 ft per second). m is the initial height of the…