Answer:
a
[tex]P(X = 4) = 0.31599[/tex]
b
[tex]P(X \ge 2) = 0.9921 [/tex]
Step-by-step explanation:
From the question we are told that
The proportion in favor of carbon tax is [tex]p = 0.72[/tex]
The sample size is n = 6
Generally the distribution of poll follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that the number answering in the affirmative is 4 is mathematically represented as
[tex]P(X = 4) = ^{6}C_4 * (0.72)^4 * (1- 0.72)^{6-4}[/tex]
=> [tex]P(X = 4) = 0.31599[/tex]
Generally the probability that the number answering in the affirmative is At least two is mathematically represented as
[tex]P(X \ge 2) = 1 - P( X < 2 ) [/tex]
[tex]P(X \ge 2) = 1- [ P(X = 0 ) + P( X = 1)] [/tex]
=> [tex]P(X \ge 2) = 1- [ [ 1 * 1 * 0.00048 ]+ [ 6 * 0.72 * 0.00172] [/tex]
=> [tex]P(X \ge 2) = 1- [ 0.00791 ] [/tex]
=> [tex]P(X \ge 2) = 0.9921 [/tex]
