Question

A soccer goalie allows a goal on average of 2.3 times per game. Make an estimate of the probability per game that the goalie records a shutout (zero goals). What assumptions did you make?

Answer #1

**Assumptions:**

- The probability of an event occurring in an interval of certain length remains same in all intervals of equal lengths
- The probability of an event occurring in an interval is independent of the probability of its occurrence in any other interval
- The probability of occurrence of an event in an interval is proportional to the length of that interval

Given that, average number of goals per game =

Average number of goals per game follows a Poisson distribution.

Probability of number of goals per game:

Hence, probability per game that the goalie records a shutout (zero goals):

The probability distribution for the number of goals the Lions
soccer team makes per game is given below.
Number
Of
Goals Probability
0 0.05
1 0.15
2 0.35
3 0.30
4 0.15
The expected number of goals per game is
0
1.57
2
2.35
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