29% 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
For part (c), the probability that less than 8 out of 12 U.S. adults favor the use of unmanned drones by police agencies is approximately \(\boxed{0.992}\).
Step 1 ：This problem is about binomial probability. The binomial distribution model is suitable for a quantitative variable that counts the number of successes in a fixed number of trials of a binary, or yes/no, outcome. Here, the 'success' is defined as a U.S. adult who favors the use of unmanned drones by police agencies. The probability of success (p) is 0.29, and the number of trials (n) is 12.
Step 2 ：For part (a), we need to find the probability that exactly 3 out of 12 adults favor the use of drones.
Step 3 ：For part (b), we need to find the probability that at least 4 out of 12 adults favor the use of drones. This is equivalent to 1 minus the probability that 3 or fewer adults favor the use of drones.
Step 4 ：For part (c), we need to find the probability that less than 8 out of 12 adults favor the use of drones. This is equivalent to the sum of the probabilities that 0, 1, 2, 3, 4, 5, 6, or 7 adults favor the use of drones.
Step 5 ：Using the given values of p = 0.29 and n = 12, we can calculate the probabilities for each part.
Step 6 ：For part (a), the probability that exactly 3 out of 12 U.S. adults favor the use of unmanned drones by police agencies is approximately \(\boxed{0.246}\).
Step 7 ：For part (b), the probability that at least 4 out of 12 U.S. adults favor the use of unmanned drones by police agencies is approximately \(\boxed{0.476}\).
Step 8 ：For part (c), the probability that less than 8 out of 12 U.S. adults favor the use of unmanned drones by police agencies is approximately \(\boxed{0.992}\).
