SOLUTION: A package of 6 bulbs are tested where the probability of an individual bulb is defective is 0.05. (That is, 5% of all the bulbs manufactured are defective). i. What is the probab

Algebra ->  Probability-and-statistics -> SOLUTION: A package of 6 bulbs are tested where the probability of an individual bulb is defective is 0.05. (That is, 5% of all the bulbs manufactured are defective). i. What is the probab      Log On


   



Question 1184024: A package of 6 bulbs are tested where the probability of an individual bulb is defective is
0.05. (That is, 5% of all the bulbs manufactured are defective).
i. What is the probability that two bulbs will be defective?
ii. What is the probability that at least one bulb will be defective?
iii. What is the probability that more than one bulb will be defective, given that at
least one is defective?
iv. Find the expected value of this distribution.
4
v. Find the standard deviation of this distribution?

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
A package of 6 bulbs are tested where the probability of an individual bulb is defective is
0.05. (That is, 5% of all the bulbs manufactured are defective).
(a) What is the probability that two bulbs will be defective?
(b) What is the probability that at least one bulb will be defective?
(c) What is the probability that more than one bulb will be defective, given that at
least one is defective?
(d) Find the expected value of this distribution.
4
(e) Find the standard deviation of this distribution?
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            I will answer  (a),  (b),  (c)  and  (d).


(a)  P = C%5B6%5D%5E2%2A0.05%5E2%2A%281-0.05%29%5E4 = %28%286%2A5%29%2F2%29%2A0.05%5E2%2A0.95%5E4 = 0.030544.    ANSWER



(b)  This probability is the COMPLEMENTARY to the probability that NO ONE bulb is defective

          P = 1+-+0.95%5E6 = 0.2649.      ANSWER


(c)  It is OBVIOUS that the probability under given condition is 1.    ANSWER



(d)  The expected value is  n*p = 0.05*6 = 0.3.     ANSWER


Solved.