Question

4) I been teaching my daughter to play soccer. The number of goals she scores follows a Poisson distribution with a mean of 5 goals per hour

A) Find the probability that she will score more than three goals in one hour..

P(x>3)=1-sum(P(0),P(1),P(2),P(3))=1-0.265=0.735

B) Find the probability that she will score exactly three goals in four hours.

Answer 1

A.)$\\ \lambda=5$

$\\ \\ Poisson~ distribution:P(X=x)=\frac{\lambda^x *e^{- \lambda}}{x!}\\\\ now\\\\ P(X>3)=1-P(x \leq3)\\\\ =1-[P(0)+P(1)+P(2)+P(3)]\\\\ =1-0.265\\\\ (use~excel~function:=POISSON(3,5,TRUE))\\\\ =0.735$

B.)

As in 1 hour 5 goals

hence in 4 hours=4*5=20 goals

$\\ \\ \lambda=20\\\\ P(X=3)=\frac{20^3 *e^{- 20}}{3!}\\\\ =0.0000$