19% 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.

(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:

(a)

Compute the probability that of 12 U.S. adults exactly 3 favor the use of unmanned drones as follows:

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)

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)

Thus, the probability that of 12 U.S. adults less than 8 favor the use of unmanned drones is 0.9996.

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step-by-step explanation: