Mathematics, 11.02.2021 22:10, elijah1090

A factory uses a special kind of lubricant to maintain its two milling machines. Weekly lubricant usage for each machine is an independent random variable (zero correlation). The first machine has a mean usage of 50.6 gallons and standard deviation of 12 gallons. The second machine has a mean usage of 64.4 gallons and standard deviation of 16 gallons. Suppose that at the beginning of the week, the factory has a total of 135 gallons of lubricant in stock. The factory will not receive any replenishment of lubricant from its supplier until the end of the week. Assume that the total lubricant usage (of the two machines combined) follows a normal distribution. What is the probability that the factory will run out of lubricant before the next replenishment arrives?

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A factory uses a special kind of lubricant to maintain its two milling machines. Weekly lubricant us...