A physics student has a 55% chance of passing their physics final. If 144 randomly selected physics students are selected, answer the following. a) Which is the correct wording for the random variable? Select an answer rv X = the probability that a randomly selected physics student passes their physics final rv X = a randomly selected physics student that passes their physics final rv X = the number of 144 randomly selected physics students that pass their physics final rv X = all physics students that pass their physics final rv X= the number of randomly selected physics students that pass their physics final rv X = a randomly selected physics student rv X = passes their physics final b) Pick the correct symbol: ? X̄ p σ N μ n X s = 144 c) Pick the correct symbol: ? X̄ σ n X s N μ p = 0.55 d) What is the probability that exactly 74 of them pass their physics final? Round final answer to 4 decimal places. e) What is the probability that less than 74 of them pass their physics final? Round final answer to 4 decimal places. f) What is the probability that more than 74 of them pass their physics final? Round final answer to 4 decimal places. g) What is the probability that exactly 81 of them pass their physics final? Round final answer to 4 decimal places. h) What is the probability that at least 81 of them pass their physics final? Round final answer to 4 decimal places. i) What is the probability that at most 81 of them pass their physics final Round final answer to 4 decimal places.
Added by Diego C.
Step 1
- X is the number of successes (students who pass) in n = 144 trials with success prob p = 0.55. - So X ~ Binomial(n = 144, p = 0.55). - Mean μ = np = 144 × 0.55 = 79.2 - Standard deviation σ = sqrt(np(1 − p)) = sqrt(144 × 0.55 × 0.45) = sqrt(35.64) ≈ 5.9716 Show more…
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