Respuesta :
Answer:
25. P(6) = 0.1721
26. P(9) = 0.0294
27. [tex]P(x\geq 4)=0.7868[/tex]
28. [tex]P(x\leq 5)=0.6009[/tex]
Step-by-step explanation:
When we have n identical and independent events with a probability p of success and (1-p) of fail, we have a Binomial distribution. So, the probability that x events are success is calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]
So, the probability that x families hardly ever pay off the balance follows a binomial distribution and it is calculated as:
[tex]P(x)=\frac{20!}{x!(20-x)!}*0.254^{x}*(1-0.254)^{20-x}[/tex]
where n is 20 and p is 0.254.
Then, the probability that exactly 6 families hardly ever pay off the balance is:
[tex]P(6)=\frac{20!}{6!(20-6)!}*0.254^{6}*(1-0.254)^{20-6}=0.1721[/tex]
The probability that exactly 9 families hardly ever pay off the balance is:
[tex]P(9)=\frac{20!}{9!(20-9)!}*0.254^{9}*(1-0.254)^{20-9}=0.0294[/tex]
The probability that at least 4 families hardly ever pay off the balance is:
[tex]P(x\geq 4)=P(4)+P(5)+...+P(19)+P(20)[/tex]
So, using the same equation to find every probability, we get:
[tex]P(x\geq 4)=0.7868[/tex]
Finally, the probability that at most 5 families hardly ever pay off the balance is:
[tex]P(x\leq 5)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)\\P(x\leq 5)=0.6009[/tex]
