Question

28​% 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

TOPIC:Binomial distribution.

Deline, p = p (of favoring the use of unnamed) deones by police agencies. = 0.28 (in decimals), n = sample size 12 , Keer, X = No. of u.s. adults who favor the use of unnamed drones by police agencies, out of the 12 selected sample. So, X ~ Bin (n = 12; p = 0.28) | it As 'p' does not rary/ from troial to trial- - 12-2 The pay of x is - P(x= x) = f (2) (0.28) * 10.72) ; Jory X=0,1,–,12 otherwise, @ we need, we P (x is exactly thosee), =P (x=3. - () (0.28)9 (0.72) - 04 25/1 (on).

& we need, (x is at least jour). = P(x+4). = 1- P(x44, = 1 - P (x = 3). = 1- [P(x=9) +P(x=1) + P (x=1) ++ (x=3) 21- (0.72)" + (13) (0.28)(0.72)" +(92) (0.28) 2 (0.7270 + C') (0.28) 3 (0,729 = 1- 0.5548. - 0.44522(And @ we need p(x is less than eight) = P(x (8) al - P (X78).

= 1- [ P(x= 8) + P (X= 9) + 8 (X=10) + P(x = 11) + P (x-12) =1-(12)(0,2098 (0.72)' + (3) (0.28) ° (0-72) I + (12) (0.28) 10 (0.722 + (12) (0.28)" (0.72) + (0.28) "? 2 1- 0.0060, - (0.9940) (Amos Answers are rounded) to your decimals.