Question

A manufacturing concern employing a large number of workers finds that, over a period of time, the average absentee rate is $2$ workers per shift. The probability that exactly $2$ workers will be absent in a chosen shift at random is

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

Answer 1

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

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,$\mu$ = 2
x = 2 (exact 2 workers)
$P(2;2)=\frac{e^{-2}{2}^2}{2!}$