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home water filtration systems customer reviews benefits motivations - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Perimeter = 2(l + w) = 2(3w + w) = 2(4w) = 8w = 60.

📌 So w = 60 / 8 = 7.5 cm.

📌 Length = 3 * 7.5 = 22.5 cm.

📌 Area = 22.5 * 7.5 = 168.75 cm².

📌 #### 168.75**Question:** A seismologist is analyzing data from 7 different seismic stations. Each station can independently detect an earthquake with a probability of \( \frac{1}{2} \). What is the probability that exactly 4 out of the 7 stations detect an earthquake?

📌 This is a binomial probability problem where we have \( n = 7 \) trials (seismic stations), each with a probability \( p = \frac{1}{2} \) of detecting an earthquake. We want to find the probability of exactly \( k = 4 \) successes (detections).

📌 The formula for the binomial probability is:

📌 P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

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