Respuesta :
Answer:
This does not mean that he would complete exactly 65 passes.
The probability that he completes exactly 65 passes is only 8.34%
65% is the number of passes he would be expected to complete in a very large sample(like 13 NFL seasons, not just a single season).
Step-by-step explanation:
There is not a 100% probability that he completes exactly 65 passes. So, it does not mean that he would complete exactly 65 passes.
How I arrived at this answer?
For each pass that he throws, either it is complete, or it is not. Since there are only two outcomes, we have a binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And [tex]\pi[/tex] is the probability of X happening.
In this problem, we have that:
There are 100 passes, so [tex]n = 100[/tex]
Each pass a 65% probability of being completed, so [tex]\pi = 0.65[/tex]
So
[tex]P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}[/tex]
[tex]P(X = 65) = C_{100,65}.(0.65)^{65}.(0.35)^{35} = 0.0834[/tex]
