Question

In a typical children's soccer game, there is one goal scored approximately every 18 minutes. The number of goals scored follows a Poisson distribution. What would the standard deviation be for the number of goals scored in an entire game? (A game consists of two 45-minute halves.)

Answer 1

Answer:

2.24

Step-by-step explanation:

The probability formula using a Poisson distribution is:

$P(k\ events) = \frac{\lambda^{k}e^{-\lambda}}{k!} \\\lambda\ is\ the\ average\ number\ of\ events\ per\ interval \\e\ is\ euler's\ number \\k\ is\ the\ number\ of\ events\ you\ want\ to\ calculate$

λ = 90 / 18 = 5 average goals per interval (interval = a game)

So if for example you were interested in the probability of making 2 goals in a game

k = 2

$P(k = 2) = \frac{5^{2}e^{-5}}{2!} = 0.084$

This was just an example,

The standard deviation is $\sqrt{\lambda}$

$\sigma = \sqrt{\lambda} \\\sigma = \sqrt{5} \\\sigma = 2.24$