Respuesta :
Using the binomial distribution, it is found that:
a) The expected number of shots until he misses is of 5.
b) You expect him to make 12 shots.
c) The standard deviation is of 1.55 shots.
What is the binomial probability distribution?
- It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q failures is:
[tex]E_f(X) = \frac{q}{1 - p}[/tex]
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem:
- A basketball player has made 80% of his foul shots during the season, hence [tex]p = 0.8[/tex].
Item a:
- Miss one shot, hence one failure, that is, [tex]q = 1[/tex].
[tex]E_f(X) = \frac{1}{0.2} = 5[/tex]
Item b:
- The player takes 15 shots, hence [tex]n = 15[/tex].
[tex]E(X) = np = 15(0.8) = 12[/tex]
Item c:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15(0.8)(0.2)} = 1.55[/tex]
You can learn more about the binomial distribution at https://brainly.com/question/14424710
