Question

A company knows on the basis of past experience that $2$% of the blades are defective. The probability of having 3 defective blades in a sample of $100$ blades is

• A. $e^{-2}{2}^2$
• B. $\frac{e^{-2}{2}^3}{3!}$
• C. $\frac{e^{-2}{2}^3}{2!}$
• D. $\frac{e^{-4}{2}^{-1}}{2!}$

Answer 1

The correct option is B $\frac{e^{-2}{2}^3}{3!}$

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(parameter)
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 $\mu$
Here,$\mu =100\times 0.02=2$
$x=3$(defective blades)
$P(3;2)=\frac{e^{-2}{2}^3}{3!}$