| Date | May 2013 | Marks available | 3 | Reference code | 13M.2.hl.TZ1.3 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
Emily walks to school every day. The length of time this takes can be modelled by a normal distribution with a mean of 11 minutes and a standard deviation of 3 minutes. She is late if her journey takes more than 15 minutes.
Find the probability she is late next Monday.
Find the probability she is late at least once during the next week (Monday to Friday).
Markscheme
Let X represent the length of time a journey takes on a particular day.
\(P(X > 15) = 0.0912112819 \ldots = 0.0912\) (M1)A1
Use of correct Binomial distribution (M1)
\(N \sim B(5,0.091 \ldots )\)
\(1 - 0.0912112819 \ldots = 0.9087887181 \ldots \)
\(1 - {(0.9087887181 \ldots )^5} = 0.380109935 \ldots = 0.380\) (M1)A1
Note: Allow answers to be given as percentages.
[5 marks]
Examiners report
There were many good answers to this question. Some students lost accuracy marks by early rounding. Some students struggled with the Binomial distribution.
There were many good answers to this question. Some students lost accuracy marks by early rounding. Some students struggled with the Binomial distribution.
