7. An order of 3000 parts is received. The probability that a part is defective

Question

7. An order of 3000 parts is received. The probability that a part is defective equals 10. Find the probability that there will be more than five defective parts. 8. A system contains 1000 components. each component fails independently of the others and the probability of its failure in one month equal 103. Find the probability that the system will function (i.e. no component will fail) at the end of one month. 9. The probability density function of a random variable X is e x20 0 otherwise (a) What is P[ls X s2]? (b) What is Fx (x), the CDF of X? (c) What is E[X], the expected value of x? (d) What is VarX], the variance of X? 10. Long distance calling plan A offers flat rate service at 10 cents per minute. Calling plan B charges 99 cents for every call under 20 minutes; for calls over 20 minutes, the charge is 99 cents for the first 20 minutes plus 10 cents for every additional minute.( duration exactly, without rounding to the next minute or even second.) If your long distance calls have exponential distribution with expected valve minutes, which plan offers a lower expec cost per call?

Explanation / Answer

P( part being defective) = 0.001

Total defective parts in 3000 is 3000*0.001 = 3

P(X>5) = 0.083

PS we are directed to solve only the first question if multiple questions are posted

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