Respuesta :
Answer:
(a) The probability that of 12 U.S. adults exactly 3 favor the use of unmanned drones is 0.2279.
(b) The probability that of 12 U.S. adults at least 4 favor the use of unmanned drones is 0.1795.
(c) The probability that of 12 U.S. adults less than 8 favor the use of unmanned drones is 0.9996.
Step-by-step explanation:
Let X = number of adults who favor the use of unmanned drones by police agencies.
The probability of the event X is, P (X) = p = 0.19
The sample of U.S. adults selected is, n = 12.
The distribution of the random variable X is Binomial.
The probability function of the Binomial distribution is:
[tex]P(X=x) = {n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...[/tex]
(a)
Compute the probability that of 12 U.S. adults exactly 3 favor the use of unmanned drones as follows:
[tex]P(X=x) = {12\choose 3}(0.19)^{3}(1-0.19)^{12-3}\\=220\times0.0069\times0.1501\\=0.2279[/tex]
Thus, the probability that of 12 U.S. adults exactly 3 favor the use of unmanned drones is 0.2279.
(b)
Compute the probability that of 12 U.S. adults at least 4 favor the use of unmanned drones as follows:
P (X ≥ 4) = 1 - P (X < 4)
= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)
[tex]=1- {12\choose 0}(0.19)^{0}(1-0.19)^{12-0}-{12\choose 1}(0.19)^{1}(1-0.19)^{12-1}\\-{12\choose 2}(0.19)^{2}(1-0.19)^{12-2}-{12\choose 3}(0.19)^{3}(1-0.19)^{12-3}\\=1-0.0798-0.2245-0.2987-0.2265\\=0.1795[/tex]
Thus, the probability that of 12 U.S. adults at least 4 favor the use of unmanned drones is 0.1795.
(c)
Compute the probability that of 12 U.S. adults less than 8 favor the use of unmanned drones as follows:
P (X < 4) = 1 - P (X ≥ 8)
= 1 - P (X = 8) - P (X = 9) - P (X = 10) - P (X = 11) - P (X = 12)
[tex]=1- {12\choose 8}(0.19)^{8}(1-0.19)^{12-8}-{12\choose 9}(0.19)^{9}(1-0.19)^{12-9}\\-{12\choose 10}(0.19)^{10}(1-0.19)^{12-10}-{12\choose 11}(0.19)^{11}(1-0.19)^{12-11}\\-{12\choose 12}(0.19)^{12}(1-0.19)^{12-12}\\=1-0.0004-0.00004-0.0000-0.0000-0.0000\\=0.9996[/tex]
Thus, the probability that of 12 U.S. adults less than 8 favor the use of unmanned drones is 0.9996.
