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The effective life of a component used in a jet-turbine aircraft engine is a random variable...

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 16 components is selected from the old process and a random sample of 25 components is selected from the improved process. What is the probability that the difference in the two sample means μ2-μ1 is at least 25 hours?

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