Respuesta :
The probability would be 0.34 or 34%.
We will set this up as a binomial distribution:
We will set this up as a binomial distribution:
We have been given that 56 percent of all American workers have a workplace retirement plan and we are also given that Americans retirement plans at workplace are independent.
To find out probability of exactly 3 out of 5 randomly selected Americans will have a retirement plan we will use Bernoulli trials.
[tex]_{r}^{n}\textrm{c}\cdot p^{r}\cdot q^{n-r}[/tex]
where p is probability of a success which in this case is Americans that have workplace retirement plans and q is probability of failure which in this case are Americans that don't have workplace retirement plans.
Upon substituting our given values in this formula we will get,
[tex]_{3}^{5}\textrm{c}\cdot0.56^{3}\cdot 0.44^{(5-3)}[/tex]
[tex]_{3}^{5}\textrm{c}\cdot0.56^{3}\cdot 0.44^{2}[/tex]
[tex]\frac{5!}{2!3!}\cdot0.175616\cdot 0.1936[/tex]
[tex]\frac{5\cdot 4\cdot 3!}{2\cdot 1\cdot 3!}\cdot 0.56^{3}\cdot 0.44^{2}[/tex]
[tex]10\cdot 0.175616\cdot 0.1936=0.339992576[/tex]
Rounding our answer to nearest hundredth we get our probability that exactly 3 out of 5 randomly selected Americans will have a retirement plan is 0.34.
