The probability that an item produced by a machine is defective is 0.002. Using the Poisson distribution, the standard deviation of the number of defective items in a lot of 1000 items is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\sqrt{2}\)
Here n = 1000 is large and p = 0.002 is small, so the number X of defective items follows a Poisson distribution with mean
\(m = np = 1000 \times 0.002 = 2\)
In a Poisson distribution the variance equals the mean, so \(\mathrm{Var}(X) = 2\) and
\(\text{standard deviation} = \sqrt{2}\)
Why the other options are incorrect
Option (2) 2 — Incorrect. 2 is the mean (and the variance); the standard deviation is its square root.
Option (3) 4 — Incorrect. 4 is the square of the mean; the variance is 2, not 4.
Option (4) 0.002 — Incorrect. 0.002 is the probability that one item is defective.