in proof testing of circuit boards, thepobability that any particular diode will

Question

in proof testing of circuit boards, thepobability 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? uppose circuit boa diodes What is the standard deviation of the number that are expected to fail? (Round your answer to three decimal places.) (b) What is the (approximate) probability that at least four 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.) diodes

Explanation / Answer

Solution:- Given probability p = 0.01, n = 200

(a) Expected value = n*p = 200*0.01 = 2

(b) Standard deviation = sqrt(n*p*q) = sqrt(200*0.01*0.99) = 1.407

(c) P(X >= 4) = 1 -(0.134 + 0.2707 + 0.2720 + 0.1814) = 0.142

(d) P(X >= 4) = 0.00144

Explanation:-

P(X = 0) = 200C0*0.01^0*0.99^200 = 0.1340

P(Y >= 4) = P(y = 4) + P(Y = 5)
= 0.0014 + 0.00004
= 0.00144

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