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Chapter 4: Q76E (page 247)

Traffic fatalities and sporting events. The relationship betweenclose sporting events and game-day traffic fatalities was investigated in the Journal of Consumer Research (December 2011). The researchers found that closer football and basketball games are associated with more traffic fatalities. The methodology used by the researchers involvedmodeling the traffic fatality count for a particular game as a Poisson random variable. For games played at the winner鈥檚 location (home court or home field), the mean number of traffic fatalities was .5. Use this information to find the probability that at least three game-day traffic fatalities will occur at the winning team鈥檚 location.

Short Answer

Expert verified

The probability that at least three game-day traffic fatalities will occur is 0.0144.

Step by step solution

01

Given information

To the Journal of Consumer Research (December 2011), The traffic fatality count for a particular game as a Poisson random variable

02

Calculation for the probability that at least three game-day traffic fatalities will occur

The random variable x is the number of game-day traffic fatalities in the winning location.

Here, x follows a Poisson distribution with a mean is 0.5

The probability that at least three game-day traffic fatalities will occur at the winning team鈥檚 location,

The probability mass function of x is,

fx=e-位位xx!where位=0.5

Px猢�3=1-Px<3=1-Px=0-Px=1-Px=2=1-e-0.50.500!-e-0.50.511!-e-0.50.522!=1-e-0.511+0.51+0.252

=1-0.60651+0.5+0.125=1-0.6065脳1.625=1-0.9855625=0.0144375鈮�0.0144

Px猢�3=0.0144

Therefore, the probability that at least three game-day traffic fatalities will occur is 0.0144.

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