Question

19​% adults favor the use of unmanned drones by police agencies. Twelve U.S. Adults are randomly selected. Find the probability that the number of U.S. Adults who favor the use of unmanned drones by police agencies is​ (a) exactly​ three, (b) at least​ four, (c) less than eight. Round answers three decimal places please!

Answer 1

0.2264

0.1795

0.2264

Explanation:

Given that:

p = 19% = 0.19

Sample size (n) = 12

Using binomial distribution formula :

p(x = x) = nCx * p^x * (1 - p)^(n-x)

1 - p = 1 - 0.19 = 0.81

Exactly 3:

p(x = 3) = 12C3 * 0.19^3 * 0.81^9

p(x = 3) = 220 * 0.001029499103502116970939

= 0.2264

B.) Atleast 4 :

P( x ≥ 4) = p(4) + p(5) + p(6) + p(7) + p(8) + p(9) + p(10) + p(11) + p(12)

To save time, we can use a binomial probability calculator :

P( x ≥ 4) = 0.1795

C.) Less than 8:

P( x < 8) = p(7) + p(6) + p(5) + p(4) + p(3) + p(2) + p(1) + p(0)

P(x < 8) = 0.9995