A-LevelMathematicsProbability and statistics9709/52 · May/June 2020 · Q48 Marks
Trees in the Redian forest are classified as tall, medium or short, according to their height. The heights can be modelled by a normal distribution with mean 40 m and standard deviation 12 m. Trees with a height of less than 25 m are classified as short.
- (a)Find the probability that a randomly chosen tree is classified as short.[3]
- (b)Of the trees that are classified as tall or medium, one third are tall and two thirds are medium. Show that the probability that a randomly chosen tree is classified as tall is 0.298, correct to 3 decimal places.[2]
- (c)Find the height above which trees are classified as tall.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] P(X < 25) = P(z < (25 - 40)/12)
- [M1] 1 - 0.8944
- [A1] 0.106
- [M1] 0.8944 divided by 3 (M1 for 1 - their (a) divided by 3)
- [A1] 0.298 AG
- [B1] 0.2981 gives z = 0.53
- [M1] (h - 40)/12 = 0.53
- [A1] h = 46.4
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