An engineer is designing a machine interface with a computer

An engineer is designing a machine interface with a computer system. The plan is to purchase the screen for the system. There are two choices of interest of differing quality. Option A will cost $18 per screen and option B will cost S 14. The following mass probability distributions for the useful life of the screens are given in the table. a) Which option is the better choice based on cost over the life of the screen? b) If the price of option A can be negotiated. how much less must it cost to make it the better Choice? 2. The diameter of a metal cylinder is a random variable having the probability density function a) What is the probabili a cylinder will have a diameter less than 493? b) Find the cumulative probability function for the diameter of the cylinder. Simplify the function! Note: You can check your work by using the function from (b) to find the answer for (a) and comparing to be sure both methods give the same answer.

Solution

1.

A.

Note that the mean lifetime is

E(x) = Sum [x P(x)]

Thus, for option A,

E(xA) = 12(0.05) + 18(0.15) + 24(0.45) + 30(0.35) = 24.6

E(xB) = 12(0.10) + 18(0.45) + 24(0.35) + 30(0.10) = 20.7

Thus, the cost/life is

cost/life A = $18/24.6 = $0.7317/month
cost/life B = $14/20.7 = $0.6763/month

Thus, OPTION B IS BETTER, as it is cheaper per month.

B.

If option A is to become $0.6763/month,

New price = 0.6763/month * 24.6 months = $16.64 [ANSWER]

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