34% 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 Nov 26, 2019
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34% 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

From the given information,

Binomial parameters, n = 12 and P=34% .034.

Here we can use binomial distribution probability.

Let ‘X’ be a binomial random variable.

Formula for binomial probability is,

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n (n-x) P (X-x) |(P) (1-p)

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Step 2

Now,

(a) P(x=3) is,

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12 |(0.34)' (1-0.34)2) P(X-3) =220x0.039304x0.02376268 -0.2054730424 P(X-3)= 0.2055

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Step 3

(b) P (at least...

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P(X 2 4) 1-P (X<4) -1-P(X-0)+P(X1)+P(X=2)+P(X=3)} 12 12 3 0.34) (1-0.34)09 (0.34) (1-0.34)(2) 3 1- 12 12 (0.34) (1-0.34)09 (0.34)' (1-0.34)2) 3 3 -1-{0.37419472421 =0.6258052758 P(X 2 4) 0.6258

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