Question

On average, five customers visit a children's department store each hour. Using Poisson distribution, calculate the probability of three customers shopping at the store.

Answer 1

The probability is of 0.1404 or 14.04%.

Explanation:

The Poisson Distribution formula is given by:

`P(x,\lambda )=(e^(-\lambda ) \lambda^(x))/(x!)`

Where:

`\lambda = \mu = \sigma^2`,

`e` is Euler's constant,

`x` is the number of successes of which we're trying to calculate the probability of occurring.

In this exercise we have that:

`\lambda = 5\\ x=3`.

Replacing in the formula we get:

`P(x=3,\lambda=5 )=(e^(-5 ) 5^(3))/(3!)=0.1404`

Therefore the probability of three customers shopping at the store in an hour is of 0.1404 or 14.04%.