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Home » The Ultimate Pin the Tail on the Donkey Challenge – Guaranteed Laughs! - inBeat

The Ultimate Pin the Tail on the Donkey Challenge – Guaranteed Laughs! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 #### 11.94

📌 A satellite orbits Earth in an elliptical path where the Earth is at one focus. The semi-major axis is 15,000 km and the eccentricity is 0.2. What is the distance from the satellite to the Earth’s center at the closest approach (perigee)?

📌 Perigee distance = \( a(1 - e) = 15000 \times (1 - 0.2) = 15000 \times 0.8 = 12,000 \, \text{km} \).

📌 A factory produces widgets with a defect rate of 3%. A quality inspector selects a random sample of 150 widgets. What is the probability that exactly 5 are defective?

📌 Use binomial distribution: \( n = 150 \), \( p = 0.03 \), \( k = 5 \).

📌 \( P(X=5) = \binom{150}{5} (0.03)^5 (0.97)^{145} \).

📌 Approximate with Poisson: \( \lambda = 150 \times 0.03 = 4.5 \).

📌 \( P(X=5) = \frac{e^{-4.5} (4.5)^5}{5!} \).

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