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Question

# Suppose that only .10% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 10,000 computers. a. What are the expected value and standard deviation of the number of computers in the sample that have the defect? b. What is the (approximate) probability that more than 10 sampled computers have the defect? c. What is the (approximate) probability that no sampled computers have the defect?

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DEFINITIONS

Formula $\textbf{Poisson probability}$:

$P(X=k)=\dfrac{\lambda^k e^{-\lambda}}{k!}$

$\textbf{Addition rule}$ for disjoint or mutually exclusive events:

$P(A\cup B)=P(A\text{ or }B)=P(A)+P(B)$

$\textbf{Complement rule}$:

$P(A’)=P(\text{not }A)=1-P(A)$

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