In proof testing of circuit boards, the probability that any particular diode wi
ID: 3276978 • Letter: I
Question
In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 200 diodes.
(a) How many diodes would you expect to fail?
diodes
What is the standard deviation of the number that are expected to fail? (Round your answer to three decimal places.)
diodes
(b) What is the (approximate) probability that at least three diodes will fail on a randomly selected board? (Round your answer to three decimal places.)
(c) If five boards are shipped to a particular customer, how likely is it that at least four of them will work properly? (A board works properly only if all its diodes work. Round your answer to four decimal places.)
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Explanation / Answer
Ans:
Binomial distribution:
n=200,p=0.01
a)Mean=200*0.01=2
2 diodes are expected to fail.
std dev=sqrt(np(1-p))=sqrt(200*0.01*(1-0.01))=sqrt(2*0.99)=1.41
b)P(k>=3)=1-P(k<=2)=1-BINOMDIST(2,200,0.01,TRUE)=0.3233
c)Probability that all diodes works i.e a circuit board work=(1-0.01)^200=0.99^200=0.134
Now,Y is Binomial distribution with n=5,p=0.134
P(Y>=4)=1-P(Y<=3)=1-BINOMDIST(3,5,0.134,TRUE)=0.0014