Answer:
2.24
Step-by-step explanation:
The probability formula using a Poisson distribution is:
[tex]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[/tex]
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
[tex]P(k = 2) = \frac{5^{2}e^{-5}}{2!} = 0.084[/tex]
This was just an example,
The standard deviation is [tex]\sqrt{\lambda}[/tex]
[tex]\sigma = \sqrt{\lambda} \\\sigma = \sqrt{5} \\\sigma = 2.24[/tex]
