| Date | May 2015 | Marks available | 2 | Reference code | 15M.2.hl.TZ1.2 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The finishing times in a marathon race follow a normal distribution with mean 210 minutes and standard deviation 22 minutes.
Find the probability that a runner finishes the race in under three hours.
The fastest \(90\% \) of the finishers receive a certificate.
Find the time, below which a competitor has to complete the race, in order to gain a certificate.
Markscheme
\(X \sim N(210,{\text{ }}{22^2})\)
\({\text{P}}(X < 180) = 0.0863\) (M1)A1
[2 marks]
\({\text{P}}(X < T) = 0.9 \Rightarrow T = 238{\text{ (mins)}}\) (M1)A1
[2 marks]
Total [5 marks]
Examiners report
This question was well done with many candidates obtaining full marks. On the whole, but quite a number misunderstood what was required in part (b) and 182 minutes was a repeated incorrect answer. It was disappointing that candidates have not noticed that this answer was clearly too small showing that candidates had not appreciated the context of the question.
This question was well done with many candidates obtaining full marks. On the whole, but quite a number misunderstood what was required in part (b) and 182 minutes was a repeated incorrect answer. It was disappointing that candidates have not noticed that this answer was clearly too small showing that candidates had not appreciated the context of the question.
