Question

1616​%

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.

Answer 1

n = 12

p = 0.16

Binomial Probabilities Table
X	Formula	P(X)
0	12!/(0!* 12!) * 0.16^0 * 0.84^12	0.1234
1	12!/(1!* 11!) * 0.16^1 * 0.84^11	0.2821
2	12!/(2!* 10!) * 0.16^2 * 0.84^10	0.2955
3	12!/(3!* 9!) * 0.16^3 * 0.84^9	0.1876
4	12!/(4!* 8!) * 0.16^4 * 0.84^8	0.0804
5	12!/(5!* 7!) * 0.16^5 * 0.84^7	0.0245
6	12!/(6!* 6!) * 0.16^6 * 0.84^6	0.0054
7	12!/(7!* 5!) * 0.16^7 * 0.84^5	0.0009
8	12!/(8!* 4!) * 0.16^8 * 0.84^4	0.0001
9	12!/(9!* 3!) * 0.16^9 * 0.84^3	0.0000
10	12!/(10!* 2!) * 0.16^10 * 0.84^2	0.0000
11	12!/(11!* 1!) * 0.16^11 * 0.84^1	0.0000
12	12!/(12!* 0!) * 0.16^12 * 0.84^0	0.0000

a) Probability of exactly 3, P(X = 3) = 0.1876

b) Probability of at least 4, P(X ≥ 4) = 1 - P(X ≤ 3)

= 1 - [ P(0)+P(1)+P(2)+P(3) ]

= 1 - [ 0.1234 + 0.2821 + 0.2955 + 0.1876 ]

= 0.1114

c) Probability of less than 8, P(X < 8) =

= P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6) +P(7)

= 0.9999