## 5. The number of goals scored in a game by a soccer team has a Poisson distribution, averaging 1.1 goalsper game.(a) What is the probability

Question

5. The number of goals scored in a game by a soccer team has a Poisson distribution, averaging 1.1 goalsper game.(a) What is the probability of the team scoring more than 3 goals combined in the next five games?

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1 month 2021-10-15T07:40:28+00:00 1 Answer 0 views 0

Step-by-step explanation: the average number of goals scored by a team every match is independent on each other and it is occurring at a fixed rate hence, u = 1.1

The probability mass function that defines a possion distribution is given as

P(x=r) = e^-u × u^x/ x!

If the team scores and average of 1.1 goals in one game, then in the next five game they will score an average of (1.1×5 = 5.5)

So therefore, for the next five games, u = 5.5

The question is to find the probability of the team scoring more than 3 goals in the next 5 games, that’s

P(x>3).

P(x>3) = 1 – P(x≤2)

The value of P(x≤2) can be gotten using a cumulative possion distribution table with the fact that u = 5.5 and x = 2.

By checking the table, we have that P(x≤2) = 0.2017

P(x>3) = 1 – 0.2017

P(x>3) = 0.7983