Please show all work for each step! s) The probability that a fluorescent light

Question

Please show all work for each step! s) 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 X = the number of light bulbs out of 20 which have a leasf 800 hours jis 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

Answer to the question is as follows:

p = .9, this is solved using binomial distribution momemt generating function

a. P(18 out of 20) = 20C18 * .9^18 *.1^2 = 0.2852

b. P(X<2) = 20C0*.9^0*.1^20 + 20C1 * .9^1 *.1^19 = 1.81*10^-18 ]

c. P(X>=3) = 1- P(X<3) = P(X=0,1,2) = 1.557*10^-16

d. The moment of generating function is
P(X=x) = nCx *(p^x)(1-p)^(n-x), where

n = 20,
x is the no. of X = no. of light bulbs out of 20 which have a useful life atleast 800 hours and
p = .9 ( as given in question)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.