Question

The auto parts department of an automotive dealership sends out a mean of 4.34.3 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 55

Answer 1

`P(X = 5) = 0.166`

Explanation:

Given

`Mean = 4.3`

`x = 5`

Required

Determine the probability that the order is 5

This question can be answered using Poisson distribution.

`P(X = x) = (\alpha ^x e^(-\alpha))/(x!)`

Where

`\alpha` is used to represent the mean

and

`\alpha = 4.3`

`x = 5`

`e = 2.71828` ---- Euler's constant

So, we have:

`P(X = x) = (\alpha ^x e^(-\alpha))/(x!)`

`P(X = 5) = (4.3^5 * 2.71828^(-4.3))/(5!)`

`P(X = 5) = (4.3^5 * 2.71828^(-4.3))/(5* 4 * 3 * 2 *1)`

`P(X = 5) = (4.3^5 * 2.71828^(-4.3))/(120)`

`P(X = 5) = (1470.08443 * 0.01356859825)/(120)`

`P(X = 5) = (19.9469850243)/(120)`

`P(X = 5) = 0.1662248752`

`P(X = 5) = 0.166` Approximated