A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2021 · Q48 Marks
Raj wants to improve his fitness, so every day he goes for a run. The times, in minutes, of his runs have a normal distribution with mean 41.2 and standard deviation 3.6.
- (a)Find the probability that on a randomly chosen day Raj runs for more than 43.2 minutes.[3]
- (b)Find an estimate for the number of days in a year (365 days) on which Raj runs for less than 43.2 minutes.[2]
- (c)On 95% of days, Raj runs for more than t minutes. Find the value of t.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] Use of Standardisation formula once, allow continuity correction, not σ², √σ.
- [M1] Appropriate area Φ, from final process, must be probability.
- [A1] AWRT
- [B1FT] 1-their (a) or correct.
- [B1FT] FT their 4SF (or better) probability, final answer must be positive integer.
- [B1] CAO, critical z value.
- [M1] Use of standardisation formula with μ, σ equated to a z-value, no continuity correction, allow σ², √σ.
- [A1]
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →