The distance advanced in a day by a tunnel boring machine, in meters, is uniformly distributed on the interval (30, 50). a) Find the mean distance. b) Find the standard deviation of the distances. c)...

The distance advanced in a day by a tunnel boring machine, in meters, is uniformly distributed on the interval (30, 50). a) Find the mean distance. b) Find the standard deviation of the distances. c) Find the probability that the distance is between 35 and 42 meters. d) Suppose the distances advanced on different days are independent. What is the probability the machine advances more than 45 meters on exactly four out of 10 days?