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A soccer goalie allows a goal on average of 2.3 times per game. Make an estimate...

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?

Math   Statistics-And-Probability   
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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):

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