Respuesta :
Answer:
[tex] P(X >9) = P(X=10) +P(X=11) [/tex]
And we can find the individual probabilities with the mas function adn we got:
[tex]P(X=10)=(11C10)(0.82)^{10} (1-0.82)^{11-10}=0.272[/tex]
[tex]P(X=11)=(11C11)(0.82)^{11} (1-0.82)^{11-11}=0.113[/tex]
And replacing we got:
[tex] P(X>9) =0.272 +0.113= 0.385[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of workers who find their jobs stressful", on this case we now that:
[tex]X \sim Binom(n=11, p=0.82)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X >9) = P(X=10) +P(X=11) [/tex]
And we can find the individual probabilities with the mas function adn we got:
[tex]P(X=10)=(11C10)(0.82)^{10} (1-0.82)^{11-10}=0.272[/tex]
[tex]P(X=11)=(11C11)(0.82)^{11} (1-0.82)^{11-11}=0.113[/tex]
And replacing we got:
[tex] P(X>9) =0.272 +0.113= 0.385[/tex]
