A-LevelMathematicsProbability and statistics9709/52 · May/June 2022 · Q47 Marks

The weights, in kg, of bags of rice produced by Anders have the distribution N(2.02, 0.03²).

(a)Find the probability that a randomly chosen bag of rice produced by Anders weighs between 1.98 and 2.03 kg.[3]
(b)The weights of bags of rice produced by Binders are normally distributed with mean 2.55 kg and standard deviation σ kg. In a random sample of 5000 of these bags, 134 weighed more than 2.6 kg. Find the value of σ.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

M1 Use of standardisation formula once with 2.02, 0.03 and either 1.98 or 2.03 substituted appropriately. Condone 0.03² and continuity correction ±0.005, not √0.03.
M1 Calculating the appropriate probability area from their z-values. (or 0.6304-0.09121 or (0.9087 – 0.5) + (0.6304 – 0.5) etc)
A1 0.539 < z < 0.5395 Only dependent upon 2nd M mark. If M0 scored SC B1 for 0.539 < z < 0.5395.
B1 0.9732 or 4866/5000 or 2433/2500 seen. [P(X> 2.6) = 134/5000 = 0.0268] [P(X<2.6) = 1 – 0.0268 =] 0.9732
M1 Use of standardisation formula with 2.6 and 2.55 substituted, no σ², √ or continuity correction.
M1 Their standardisation formula with values substituted equated to z-value which rounds to ±1.93.
A1 AWRT 0.0259 or 5/193. If M0 earned, SC B1 for correct final answer. [σ = 0.0259]

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