In proof testing of circuit boards, the probability that any particular diode wi

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. How many diodes would you expect to fail? What is the standard deviation of the number that are expected to fail? (Round your answer to three decimal places.) What is the (approximate) probability that at least five diodes will fail on a randomly selected board? (Round your answer to three decimal places.) 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.)

Explanation / Answer

A) E(X) = X*P(X)

HERE X = 200

P(X) = 0.01

E(X) = 200*0.01 = 2

VAR(X) = E(X^2) - E(X)^2

VAR(X) = 400 - 4 = 396

STANDARD DEV = VAR(X)^(1/2) = 19.8

B)AT LEAST 5 WILL FAIL = 1 - P(LESS THEN 5 WILL FAIL)

P( KESS THE 5 WILLFAIL ) = P(0)+P(1)+P(2)+P(3)+P(4)

CALCULATING THIS WE WILL GET VERY SMALL NUMBER BECAUSE N = 200 WHICH IS VERY LARGE

HENCE THE ANSWER WILL BE 0.99

C)N = 5

AT LEAST 4 = P(4) + P(5)

HERE WE WILLCALCULATE FOR WORKING PROPERLY

P(4) = 5C4*(0.133)^1*(0.867)4 = 0.375

P(5) = 5C5*(0.133)^0*(0.867)^5 = 0.489

ADDING BOTH WE WILL GET THE ASWER = 0.864

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