Discussion
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are
Answer: A
The mean and the variance are 3 and 3.
The Poisson parameter is the expected number of defectives in the box:
\[ \lambda = np = 200 \times 0.015 = 3 \]
A Poisson distribution has mean and variance both equal to \(\lambda\), so both are 3.
\(\sqrt{3}\) is the standard deviation, not the variance, and the mean is not \(\sqrt{3}\) either. 0.015 is the probability that a single component is defective, not the count in a box of 200. '3 and 9' squares the mean to get the variance, which confuses the Poisson variance \(\lambda\) with \(\lambda^{2}\).
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