A-LevelMathematicsProbability and statistics9709/62 · May/June 2018 · Q36 Marks

(i) The volume of soup in Super Soup cartons has a normal distribution with mean μ millilitres and standard deviation 9 millilitres. Tests have shown that 10% of cartons contain less than 440 millilitres of soup. Find the value of μ. (ii) A food retailer orders 150 Super Soup cartons. Calculate the number of these cartons for which you would expect the volume of soup to be more than 1.8 standard deviations above the mean.

(i)The volume of soup in Super Soup cartons has a normal distribution with mean μ millilitres and standard deviation 9 millilitres. Tests have shown that 10% of cartons contain less than 440 millilitres of soup. Find the value of μ.[3]
(ii)A food retailer orders 150 Super Soup cartons. Calculate the number of these cartons for which you would expect the volume of soup to be more than 1.8 standard deviations above the mean.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[B1] (i) ±1.282 seen
[M1] (i) Standardisation equation with 440, 9 and μ, equated to a z-value, (not 1 - z-value or probability e.g. 0.1841, 0.5398, 0.6202, 0.8159)
[A1] (i) Correct answer rounding to 452, not dependent on B1
[B1] (ii) P(z > 1.8) = 1 – 0.9641 = 0.0359
[M1] (ii) p x 150, 0 < p < 1
[A1FT] (ii) Accept either 5 or 6, not indicated as an approximation, e.g. ~, about FT their p × 150, answer as an integer

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