46. A machine makes a product that is screened (inspected 100 percent) before being shipped. The measuring

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46. A machine makes a product that is screened (inspected 100 percent) before being shipped. The measuring instrument is such that it is difficult to read between 1 and 113

(coded data). After the screening process takes place, the measured dimension has density

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(a) Find the value of k.

(b) What fraction of the items will fall outside the twilight zone (fall between 0 and 1)?

(c) Find the mean and variance of this random variable.

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