Question

1. A review of the extensive data available in the computer files of House Heating Gas Distributors revealed that the useful lifetime X of an expensive mechanical component widely used by its maintenance department is a normally distributed random variable with mean and standard deviation equal to 10,600.0 hours and 400.0 hours respectively. (a) Suppose that a component is randomly selected from the stock available in the warehouse. What is the probability that the lifetime X of this component exceeds 10,000.0 hours? Write down the probability density function of X. Then draw the probability density function of X, neatly and clearly, and indicate the area that corresponds to this probability. (b) Compute (i) the lower quartile and (ii) upper decile of the probability distribution of X (c) Let M represent the mean lifetime of a random sample of sixteen components (i)Find the mean and standard deviation of the probability distribution of (ii) Write down the probability density function of M. (iii) Draw, neatly and clearly, the probability density function of X and M on the same diagram. (iv) Compute the probability that M differs from the mean by more than 200.0 hours. (d) Let T be the sum of the lifetimes of 100 components used in a given year. Find the mean and variance of T. Then compute the probability that T exceeds 1,066,000.0 hours. Draw the probability density function of T and indicate the area that corresponds to this probability.

Answer 1

Paga No. ーー JEK210000).1.KKIocoo) t- PC2) 20000) 0.9332- de

Page No. 0.61 LOO mdyu 2.

6oo 19 600 oyoo べto 500 LOO 2 2-2

1-0.9722+.0222 00228 0022 0.056 P(2) L0 10 0.9332 tatel tb?