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.

Question

asked May 18, 2020 200k views

1 Answer

Ian Dallas · Answer 1 · 2020-05-25T07:53:26+0000

Answer:

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:

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

is Euler's constant,

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%.