Question

In a poll conducted by a survey firm, 82% of respondents said that their jobs were sometimes or always stressful. Eleven workers are chosen at random for the Binomial experiment. What is the probability that more than 9 of them find their jobs stressful

Answer 1

Answer:

$P(X >9) = P(X=10) +P(X=11)$

And we can find the individual probabilities with the mas function adn we got:

$P(X=10)=(11C10)(0.82)^{10} (1-0.82)^{11-10}=0.272$  

$P(X=11)=(11C11)(0.82)^{11} (1-0.82)^{11-11}=0.113$  

And replacing we got:

$P(X>9) =0.272 +0.113= 0.385$

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:  

$X \sim Binom(n=11, p=0.82)$  

The probability mass function for the Binomial distribution is given as:  

$P(X)=(nCx)(p)^x (1-p)^{n-x}$  

Where (nCx) means combinatory and it's given by this formula:  

$nCx=\frac{n!}{(n-x)! x!}$  

We want to find the following probability:

$P(X >9) = P(X=10) +P(X=11)$

And we can find the individual probabilities with the mas function adn we got:

$P(X=10)=(11C10)(0.82)^{10} (1-0.82)^{11-10}=0.272$  

$P(X=11)=(11C11)(0.82)^{11} (1-0.82)^{11-11}=0.113$  

And replacing we got:

$P(X>9) =0.272 +0.113= 0.385$