The effective life of a component used in a jet-turbine aircraft engine is a random variable with mean 5000 hours and standard deviation 40 hours. The distribution of effective life is fairly close to a normal distribution. The engine manufacturer introduces an improvement into the manufacturing process for this component that increases the mean life to 5050 hours and decreases the standard deviation to 30 hours. Suppose that a random sample of n1 =16 components is selected from the “old” process and a random sample n2 =25 components is selected from the “improved” process. a. What is the probability that the difference in the two sample means x̄1 - x̄2 is at least 25 hours? Assume that the old and improved processes can be regarded as independent populations. b. Plot the density curve.

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