A-LevelMathematicsProbability and statistics9709/62 · May/June 2017 · Q59 Marks
The lengths of videos of a certain popular song have a normal distribution with mean 3.9 minutes. 18% of these videos last for longer than 4.2 minutes.
- (i)Find the standard deviation of the lengths of these videos.[3]
- (ii)Find the probability that the length of a randomly chosen video differs from the mean by less than half a minute.[4]
- (iii)The lengths of videos of another popular song have a normal distribution with the same mean of 3.9 minutes but the standard deviation is twice the standard deviation in part (i). The probability that the length of a randomly chosen video of this song differs from the mean by less than half a minute is denoted by p. Without any further calculation, determine whether p is more than, equal to, or less than your answer to part (ii). You must explain your reasoning.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- M1 Standardising, not square root of σ, not σ²
- B1 Accept 0.915 ≤ ± z ≤ 0.916 seen
- A1 Correct final answer (allow 20/61 or 75/229)
- M1 Standardising attempt with 3.4 or 4.4 only, allow square root of σ, or σ²
- A1 0.936 < Φ < 0.937 or 0.063 < Φ ≤ 0.064 seen
- M1 Correct area 2Φ – 1OE i.e. Φ = − (1 – Φ), linked to final solution
- A1 Correct final answer from 0.9363 < Φ ≤0.9365
- *B1 No calculations or calculated values present e.g. (σ= )0.656 seen Reference to spread or z value required
- DB1 Dependent upon first B1
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