During a single day at radio station WMZH, the probability that a particular song is played is 0.52 . What is the probability that this song will be played on at least 5 days out of 7 days? Round your answer to the nearest thousandth. Answer:

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Introduction: To solve this problem, we need to use the binomial probability formula, which is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where: - P(X = k) is the probability of k successes in n trials, - C(n, k) is the number of combinations of n items taken k at a time, - p is the probability of success on a single trial, and - (1-p) is the probability of failure on a single trial. In this case, a ＂success＂ is the song being played on a given day, and we want to find the probability of at least 5 successes in 7 days.Calculate Probability of 5 Days: First, we calculate the probability of the song being played exactly 5 days out of 7. We use the binomial coefficient C(7, 5) to determine the number of ways to choose 5 days out of 7, and then multiply by the probability of success raised to the power of 5 and the probability of failure raised to the power of 2. C(7, 5) = 7! / (5! * (7-5)!) = 21 P(X = 5) = 21 * (0.52)^5 * (1-0.52)^2Calculate Probability of 6 Days: Next, we calculate the probability of the song being played exactly 6 days out of 7. C(7, 6) = 7! / (6! * (7-6)!) = 7 P(X = 6) = 7 * (0.52)^6 * (1-0.52)^1Calculate Probability of 7 Days: Then, we calculate the probability of the song being played all 7 days. C(7, 7) = 7! / (7! * (7-7)!) = 1 P(X = 7) = 1 * (0.52)^7 * (1-0.52)^0Calculate Total Probability: Now, we add the probabilities of the song being played exactly 5, 6, and 7 days to get the total probability of it being played at least 5 days out of 7. P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7)Perform Calculations and Sum: We perform the calculations for each case and sum them up. P(X = 5) = 21 * (0.52)^5 * (0.48)^2 P(X = 5) ≈ 21 * 0.0387 * 0.2304 P(X = 5) ≈ 0.1975  P(X = 6) = 7 * (0.52)^6 * (0.48)^1 P(X = 6) ≈ 7 * 0.0202 * 0.48 P(X = 6) ≈ 0.0679  P(X = 7) = 1 * (0.52)^7 * (1)^0 P(X = 7) ≈ 1 * 0.0105 P(X = 7) ≈ 0.0105  P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) P(X >= 5) ≈ 0.1975 + 0.0679 + 0.0105 P(X >= 5) ≈ 0.2759Finalize Answer: Finally, we round the answer to the nearest thousandth as requested. P(X >= 5) ≈ 0.276

During a single day at radio station WMZH, the probability that a particular song is played is $0$ . $52$ . What is the probability that this song will be played on at least $5$ days out of $7$ days? Round your answer to the nearest thousandth. $\newline$ Answer:

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During a single day at radio station WMZH, the probability that a particular song is played is $0$ . $52$ . What is the probability that this song will be played on at least $5$ days out of $7$ days? Round your answer to the nearest thousandth. $\newline$ Answer: