1 Let X the number of flaws on the surface of a randomly sel

1) Let X, the number of flaws on the surface of a randomly selected boiler of a certain type, have a Poisson distribution with parameter ? = 5. Use the cumulative Poisson probabilities from the Appendix Tables to compute the following probabilities. (Round your answers to three decimal places.)

a) P(9 ? X)

b)  P(5 ? X ? 8)

c) P(5 < X < 8)

2) 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) 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 six 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.)

Solution

1)a)P(x=9) = 0.0363

P(X<=9) = 0.9682 (The symbol is not clear so i give for all)

P(X>=9) = 0.0681

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b)  P(5 ? X ? 8) = P(5<=x<=8) = 0.9319-0.4405

= 0.4914

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c) c) P(5 < X < 8) =0.8666 -0.6159

= 0.2509

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Q.NO2

X- the no of random variables fail follow abinomial distribution.

a) Mean = np = 2

Variance =npq = 1.98

std dev = 1.407

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b) P(X>=6) = 0.01602

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c) P(atleast 4 works out of 5)

n =5 here and p = 0.01

P(atleast 4 works out of 5) = P(x<=1) =0.9990