Large reservoirs of oil found underground are under very high pressure, which allows the oil to be pumped to the surface. All oil fields contain some water, and as water is pumped back into a well to maintain high pressure, the water content increases. Suppose the proportion of water X in a randomly selected barrel of oil pumped to the surface has a normal distribution with mean = 0.12 and standard deviation = 0.025. (a) What is the probability that a randomly selected barrel of oil has a proportion of water less than 0.12? Give your answer to at least one decimal place. P (proportion of water is less than 0.12) = (b) What is the probability that a randomly selected barrel of oil has a proportion of water between 0.15 and 0.17? Give your answer to at least four decimal places. P (proportion of water is between 0.15 and 0.17) = (c) The higher the proportion of water in oil, the more expensive it is to separate the oil from the water. If the proportion of water is greater than 0.20, then the well is too expensive to operate and maintain. What is the probability that a randomly selected well is too expensive? Give your answer to at least four decimal places. P (randomly selected well is too expensive) =