Con?dence interval for the mean age

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Answer to each of the following questions.

(a) To determine the average age of its customers, a large manufacturer of men's clothing took a random sample of 200 customers and found ¯ X = 36. If you know σ = 12, ?nd a 95% con?dence interval for the mean age µ of all the customers.

(b) The joint probability function of X and Y is given as follows. Calculate and tabulate P(X|Y ) for Y = 1. Is it the same as the unconditional distribution P(X)? What does this indicate about the independence of X and Y ? XY 0 1 2 0 .10 .20 .10 1 .15 .20 .25

(c) A barometer manufacturer, in testing a very simple model, found that it sometimes erred: on rainy days it erroneously predicted "no rain" 10% of the time; and on the days when it didn't rain, it erroneously predicted "rain" 30% of the time. In a small town on the west coast, it rains 40% of the days in September. On a day in September, its barometer prediction turns out to be "rain." Now what is the chance it will actually rain?

Reference no: EM132342746

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