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The sum of two uniform random numbers. Generate two random numbers between 0 and 1 and take Y to be their sum. Then Y is a continuous random variable that can take any value between 0 and 2. The density curve of Y is the triangle shown in given Figure.
(a) Verify by geometry that the area under this curve is 1.
(b) What is the probability that Y is less than 1? Sketch the density curve, shade the area that represents the probability, then find that area. Do this for (c) also.
(c) What is the probability that Y is greater than 0.6?
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A machine is designed to produce gaskets with a mean inside diameter of 0.375 Inch. State the rejection region for the test statistic. Use an α = 0.01 level of significance. Suppose that a random sample of n = 20 gaskets had a mean of 0.373 inches. C..
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