22​% 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.

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Asked Oct 14, 2019
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22​% 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.
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Expert Answer

Step 1

Consider,

X be a random variable (who favor use of unmanned drones by police agencies) that follows binomial distribution with probability of success 0.22 and number of trials are 12.

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-B(n 12, p 0.22) 12 (0.22) (0.78) 1,2, 3,...... 12-x ,12 f(x) x | 0,

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Step 2

Thus, the required probability can be calculated as;

a)

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xB(n 12, p 0.22) 12 P(X=3) (0.22) (0.78) 0.25

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Step 3

b)

...
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B(n-12, p 0.22) x 12 12 P(X24)=E 12-i (0.22)' (0.78)i (4,5,6.,.... 1 i i=4 0.261

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