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Assessment Schedule Statistics and Modelling: Use probability distribution models to solve straightforward problems (90646) Achievement Use probability distribution models to solve straightforward problems. Q a b Normal distribution (µ = 192, σ = 28): P(X > 180) = P(Z > - 0.429) = 0.666 (G.C. Normal distribution (µ = ?, σ = 0.6): P(X > 133) < 0.01 z = 2.33 Achievement with Merit Use probability distribution models to solve problems. Achievement with Excellence Use and justify probability distribution models to solve complex problems. Judgement Accept CAO without any working. A: 1a or 1b M: 1b 133 2.33 0.6 Re-arranging to solve gives: µ = 131.6 grams Accept µ consistent with z score which may vary with rounding, Answer should be rounded to at least 4 sig. fig. 1 Ignore units c Sufficiency Award a single grade for each question holistically in reference to the achievement criteria Poisson distribution (λ = ?): P(X ≥ 1) = 0.26 P(X = 0) = 0.74 e-λ = 0.74 λ = 0.301 So the mean number of declined credit card transactions per hour is 0.301. Accept λ consistent with with rounding E: 1c Achievement Use probability distribution models to solve straightforward problems. Q a b c 2 Binomial distribution (n = 20, p = 0.1): P(X ≥ 2) = 0.608 (G.C.) Binomial distribution (n = 10, p = 0.25): P(X ≤ 5) = 0.980 (G.C.) Binomial distribution (n = 10, p = 0.2): P(X ≤ 5) = 0.994 (G.C.) Achievement with Merit Use probability distribution models to solve problems. Achievement with Excellence Use and justify probability distribution models to solve complex problems. Judgement Accept CAO without any working. P(no more than half black and no more than half white zPhones are faulty) = 0.980 x 0.994 = 0.974 Accept CAO without any working. Sufficiency Award a single grade for each question holistically in reference to the achievement criteria A: 2a or 2b M: 2b E: 2c Select distribution: X can be modelled by Poisson distribution Justify: Two required Occurrence of complaints occurs randomly Each complaint is independent Complaints cannot occur simultaneously The probability of a complaint is proportional to the length of the time interval Parameter(s): For this data, λ is estimated to be 1.25, as the mean number of complaints per month is estimated to be 1.25. Distribution must be selected, justified in context and defined in reference to its parameter(s) Or equivalent for λ Achievement Use probability distribution models to solve straightforward problems. Q a b Achievement with Merit Use probability distribution models to solve problems. Achievement with Excellence Use and justify probability distribution models to solve complex problems. Poisson distribution (λ = 3): P(X ≤ 1) = 0.199 (G.C.) Poisson distribution (λ = 3): P(X = 0) = 0.05 (G.C.) Judgement Accept CAO without any working. Binomial distribution (n = 5, p = 0.05): P(X = 2) = 0.021 (G.C.) c Accept CAO without any working. µT = 6 x 192 + 4 x 285 = 2292 seconds = 38 minutes 12 seconds σT = 6 282 4 422 = 108.4 seconds = 1 minute 48.4 seconds Or equivalent Or equivalent P(X < 2300) = P(Z < 0.074) = 0.529 (G.C.) Overall grade A: 3a or 3b M: 3b E: 3c Normal distribution: 3 Sufficiency Award a single grade for each question holistically in reference to the achievement criteria Achievement Achievement with Merit Achievement with Excellence Use probability distribution models to solve straightforward problems. Use probability distribution models to solve problems. Use and justify probability distribution models to solve complex problems. At least two questions graded A (or higher) Two questions graded M (or higher) Two questions graded E