Respuesta :
Answer:
P(x > 10) = 0.6981.
Step-by-step explanation:
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}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations 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 p is the probability of X happening.
In this question:
[tex]n = 14, p = 0.8[/tex]
P(x>10)
[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 11) = C_{14,11}.(0.8)^{11}.(0.2)^{3} = 0.2501[/tex]
[tex]P(X = 12) = C_{14,12}.(0.8)^{12}.(0.2)^{2} = 0.2501[/tex]
[tex]P(X = 13) = C_{14,13}.(0.8)^{13}.(0.2)^{1} = 0.1539[/tex]
[tex]P(X = 14) = C_{14,14}.(0.8)^{14}.(0.2)^{0} = 0.0440[/tex]
[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.2501 + 0.2501 + 0.1539 + 0.0440 = 0.6981[/tex]
So P(x > 10) = 0.6981.
