Football team makes in average 2 touchdowns per game.
Use Poisson distribution to find probability that this team
will make 5 touchdowns in the next 3 games (adjust ë)
Tip: use Poisson Appendix Table or Excel function Poisson(x, ë, false)
for x=5 and ë = 2*3 = 6 per 3 games.
To find the probability that the team will make 5 touchdowns in the next 3 games using the Poisson distribution, we need to calculate the parameter λ (lambda) for the distribution. In this case, λ is given by the average number of touchdowns per game multiplied by the number of games.
Given that the team makes an average of 2 touchdowns per game and we have 3 games, λ = 2 * 3 = 6.
Now, we use the Poisson distribution formula to calculate the probability of making 5 touchdowns:
P(x; λ) = (e^(-λ) * λ^x) / x!
where P(x; λ) is the probability of getting exactly x touchdowns in a given number of games, e is the base of the natural logarithm (~2.71828), and x! denotes the factorial of x.
Substituting the values into the formula:
P(5; 6) = (e^(-6) * 6^5) / 5!
Before we proceed further, it's important to note that the e^(-6) term is a constant value that can be found in the Poisson distribution table or using the Excel function EXP(-6).
Using the Excel function POISSON(5,6,FALSE) or referring to the Poisson distribution table for λ = 6 and x = 5, we can find that the probability is approximately 0.146.
Therefore, the probability that the team will make 5 touchdowns in the next 3 games is approximately 0.146.
To use the Poisson distribution to find the probability that the football team will make 5 touchdowns in the next 3 games, we need to adjust the average rate (λ) of touchdowns per game to λ' for the number of games being considered.
Given that the team makes an average of 2 touchdowns per game, we can calculate the adjusted average rate as follows:
λ' = average rate per game * number of games
= 2 * 3 (since we are considering 3 games)
= 6 touchdowns in 3 games
Now we can use the Poisson distribution function, which gives the probability of a specific number of events occurring in a given interval, to find the probability of the team making exactly 5 touchdowns in the next 3 games.
You can use the Poisson distribution function either with a Poisson Appendix Table or an Excel function.
Using the Excel function, you would use the Poisson(x, λ', false) function, where x is the specific number of touchdowns you want to calculate the probability for (in this case, 5), and λ' is the adjusted average rate (in this case, 6).
So, the Excel function would be Poisson(5, 6, false).
Alternatively, if you prefer to use a Poisson Appendix Table, you would find the row that corresponds to λ' = 6 and look for the column that corresponds to x = 5. The intersection of this row and column would give you the probability.
I hope this helps you in finding the probability that the football team will make 5 touchdowns in the next 3 games using the Poisson distribution.