A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2018 · Q48 Marks
It is given that X ~ N(31.4, 3.6). Find the probability that a randomly chosen value of X is less than 29.4.
- (a)It is given that X ~ N(31.4, 3.6). Find the probability that a randomly chosen value of X is less than 29.4.[3]
- (b)The lengths of fish of a particular species are modelled by a normal distribution. A scientist measures the lengths of 400 randomly chosen fish of this species. He finds that 42 fish are less than 12 cm long and 58 are more than 19 cm long. Find estimates for the mean and standard deviation of the lengths of fish of this species.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] Standardise, no cc, must have sq rt.
- [M1] Obtain 1 - prob
- [A1] Correct final answer
- [M1] Eqn with μ,σ and a z-value. Allow cc, wrong sign, but not √σ or σ²
- [B1] Any form with z value rounding to ±1.25
- [B1] Any form with z value rounding to ±1.06
- [M1] Solve 2 equations in μ, σ eliminating to 1 unknown
- [A1] Correct answers
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