4.(25 pts) The probability that a fluorescent light has a useful life of at a. F

Question

4.(25 pts) The probability that a fluorescent light has a useful life of at a. Find the probability that exactly 18 out of 20 such bulbs will b. Find the probability that less than 2 out of 20 such bulbs will c. Find the probability that at least 3 out of 20 will not have a d. Let the number of light bulbs out of 20 which have a least 800 hours is 0.9 have a useful life of at least 800 hours. have a useful life of at least 800 hours. useful life of at least 800 hours. useful life of at least 800 hours. State the moment-generating function for X

Explanation / Answer

Let X be the number of fluorescent light that has a useful life of atleast 800 hours is 0.9

P(success) p = 0.9 ,q =1-p =1-0.9= 0.1

a)probablity that exactly 18 out of 20 bulbs will have a useful life of atleast 800 hrs is:

P( 18 will have useful life) =P(X=18) = 0.285

b)probablity that less than 2 out of 20 bulbs will have a useful life of atleast 800 hrs is:

P( less than 2 out of 20) =P(X<=2)= 0.999

c)

P(at least 3 will not have a useful life) = P(at most 17 will have useful life) = 0.99

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