Question

If $3$% of electric bulbs manufactured by a company are defective, the probability that a sample of $100$ bulbs has no defective bulbs is

• A. 0
• B. $e^{-3}$
• C. $1-e^{-3}$
• D. $3e^{-3}$

Answer 1

The correct option is B $e^{-3}$

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 $\mu$
$\mu =100\times 0.03=3$
$x=0$ (No defective bulbs)
$P(0;3)=\frac{e^{-3}{3}^0}{0!}$
$P(0;3)=e^{-3}$