Question

If $3$% of electric bulbs manufactured by a company are defective, the probability that in a sample of $100$ bulbs exactly five are defective is

• A. $\frac{e^{-0.03}(0.03{)}^5}{5!}$
• B. $\frac{e^{-0.03}(0.3{)}^5}{5!}$
• C. $\frac{e^{-3}{3}^5}{5!}$
• D. $\frac{e^{-0.03}{3}^5}{5!}$

Answer 1

Answer: (C)

$\frac{e^{-3}{3}^5}{5!}$

By using Poisson distribution,

$P(x;\mu )=\frac{e^{-\mu }{\mu }^x}{x!}$

$\mu$: The mean number of successes that occur in a specified region.

$x:$The actual number of successes that occur in a specified region.

$P(x;$ $\mu$): The Poisson probability that exactly x successes occur in a Poisson experiment, when the mean number of successes is $\mu$.

$\mu =100\times 0.03=3$

$x=5$

$P(5;3)=\frac{e^{-3}{3}^5}{5!}$