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QUIZ 4-2 - = T P X> 44.5 = P> 6 40 5 44 Z = P Z> 0.75...

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STAT 400 Spring 2011 Version C Name ANSWERS . Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. (5) Alex sells “ Exciting World of Statistics ” videos over the phone to earn some extra cash during the economic crisis. Only 10% of all calls result in a sale. Assume that the outcome of each call is independent of the others. Use Normal approximation to find the probability that Alex would make at least 45 sales if he makes 400 phone calls. Binomial, p = 0.10, n = 400. Need P ( X 45 ) = ? onesans μ = n p = 400 0.10 = 40 . σ 2 = n p ( 1 – p ) = 400 0.10 0.90 = 36 . σ = 6 . twosans 0.5 correction: want 45, do not want 44. P ( X > 44.5 ) = ?
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Unformatted text preview: ) = ? T P ( X > 44.5 ) = P -> 6 40 5 . 44 Z = P ( Z > 0.75 ) = 1 – Φ ( 0.75 ) = 0.2266 . ( Binomial distribution, n = 400, p = 0.10, P ( X ≥ 45 ) = 0.22367. ) 2. The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page. Find the probability that there would be at most 40 typos in a 24-page paper. (Use Normal approximation.) Need P(X ≤ 40) = ? o μ = λ = 24 ⋅ 1.5 = 36. σ = λ = 6. t 0.5 correction: want 40, do not want 41. P(X < 40.5) = ? T P(X < 40.5) = P -< 6 36 5 . 40 Z = P(Z < 0.75) = Φ (0.75) = 0.7734 . ( Poisson distribution, λ = 36, P(X ≤ 40) = 0.7771. )...
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