Answer:
1) Binomial distribution with n=5 and p=0.84.
2) Attached. Skewed.
3) C. Skewed right
4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.
Step-by-step explanation:
1) A binomial distribution for this case can be constructed with the parameters n=5 and p=0.84.
The probability of k adults from the sample respond Yes is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}=\dbinom{5}{k} 0.84^{k}\cdot 0.16^{5-k}[/tex]
[tex]P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=1*1*0.0001=0.0001\\\\\\P(x=1) = \dbinom{5}{1} p^{1}(1-p)^{4}=5*0.84*0.0007=0.0028\\\\\\P(x=2) = \dbinom{5}{2} p^{2}(1-p)^{3}=10*0.7056*0.0041=0.0289\\\\\\P(x=3) = \dbinom{5}{3} p^{3}(1-p)^{2}=10*0.5927*0.0256=0.1517\\\\\\P(x=4) = \dbinom{5}{4} p^{4}(1-p)^{1}=5*0.4979*0.16=0.3983\\\\\\P(x=5) = \dbinom{5}{5} p^{5}(1-p)^{0}=1*0.4182*1=0.4182\\\\\\[/tex]
2) The graph is attached.
The shape is skewed to the right. This is due to the value of p being close to 1.
The sample space is [0,1,2,3,4,5] and the biggest values have the highest probabilities.
3) The shape is skewed right.
4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.
The value k=2 can also be considered unusual as it has an associated probability of 2.8%.
