Question

12. Suppose that the number of goals scored by the King Philip High School soccer team is Poisson distributed with a mean (u) of 3.2 per game. If we randomly attended a game last season, what is the probability we saw King Philip shut out? (Note: being shut out means King Philip scored no goals) EXCEL COMMAND

Answer 1

Here we are given that, the number of goals scored by the king Philip High school soccer team is Poisson distribution with mean 3.2 per game.

Now, in this case we want to find.the probability that king Philip Shut out i.e. king Philip scored no goals.

Let us assume that a random variable X .

Where, X = numbers of goals scored by the king Philip High school soccer team.

Thus , here X follows the Poisson distribution i.e.

Now, we find the required probability as follows.

xup (3.2)

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we that the - دل -lu x ou x! where pm of of poisson know distribution PLX - - x = 0,112 u do M ii the parameters here given that M=302 Now, we find probability that King Philips scored no goals joco p [X=0] therefore, P[x=0] = M o ! -M e = è u 3°2 PEX=0] = { u=3.2 2 } P [X=0] = 004 076

Thus the required probability is 0.04076.