we are to find: the probability that the number of U.S. adult who thinks that the government should help fight childhood obesity is:
(a) exactly two (b) at least four
Answer:
P(X =2) = 0.3160
P(X ≥ 4) = 0.1656
Step-by-step explanation:
From the given information:
The population proportion = 39/100 = 0.39
the sample size = 6
(a) The required probability that exactly two adults fight childhood obesity out of the six is:
[tex]P(X=2) = (^6_2) (0.39)^2 (1-0.39)^{6-2}[/tex]
[tex]P(X=2) = \dfrac{6!}{2!(6-2)!} (0.39)^2 (1-0.39)^{4}[/tex]
[tex]P(X=2) = 15 \times 0.1521 \times 0.1385[/tex]
P(X =2) = 0.3160
(b)
The probability that at least 4 adults did is:
P( X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6)
[tex]P( X \ge 4) =(^6_4) (0.39)^4 (1-0.39)^{6-4} + (^6_5) (0.39)^5 (1-0.39)^{6-5}+ (^6_6) (0.39)^6 (1-0.39)^{6-6}[/tex]
[tex]P( X \ge 4) =(\dfrac{6!}{4!(6-4)!}) (0.39)^4 (1-0.39)^{2} +(\dfrac{6!}{5!(6-5)!}) (0.39)^5 (1-0.39)^{1}+ (\dfrac{6!}{6!(6-6)!}) (0.39)^6 (1-0.39)^{0}[/tex]
P(X ≥ 4) = 0.1291 + 0.0330 + 0.0035
P(X ≥ 4) = 0.1656
