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

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(52797) (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?
~~~~~~~~~~~~~~~

I will answer (a), (b), (c) and (d).

(a)  P =  =  = 0.030544.    ANSWER



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

          P =  = 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.

RELATED QUESTIONS
A box contains 1000 light bulbs. The probability that there is at least 1 defective bulb (answered by Boreal)

A quality control engineer at a light bulb plant estimates that 1% of the bulbs it sells... (answered by lynnlo)

Ten light bulbs are chosen from a manufacturing lot and tested. If the probability of any (answered by Boreal)

Light bulbs from production lines are tested. Of the 150 bulbs tested, 7 were detective. (answered by ewatrrr)

A lot contains 20 electric bulbs 5 of which are defective. In how many ways can 4 bulbs... (answered by ewatrrr)

The probability that I find defective bulb in a supermarket display is 0.25. Suppose I... (answered by Fombitz)

Three light bulbs are selected in succession from 15 bulbs of which 5 are defective. If... (answered by ikleyn)

Hello, I need help with this question One light bulb is selected at random from a lot... (answered by math_helper)