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?

Answer: P (x>3) = 0.7983

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