If the number of defective items selected at random from a parts inventory is considered to follow a binomial distribution with n = 50 and p = 0.10, the standard deviation of the number of defective parts is:
A) 5
B) 4.5
C) 45
D) about 2.12

Question

Quizplus · Accepted Answer

The standard deviation ($\sigma$) of a binomial distribution is calculated using the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials and $p$ is the probability of success on each trial. Substituting $n = 50$ and $p = 0.10$ gives $\sigma = \sqrt{50 \cdot 0.10 \cdot (1-0.10)} = \sqrt{50 \cdot 0.10 \cdot 0.90} = \sqrt{4.5} \approx 2.12$.

If the Number of Defective Items Selected at Random from a Parts