| Date | May 2018 | Marks available | 2 | Reference code | 18M.1.sl.TZ1.13 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 13 | Adapted from | N/A |
Question
Malthouse school opens at 08:00 every morning.
The daily arrival times of the 500 students at Malthouse school follow a normal distribution. The mean arrival time is 52 minutes after the school opens and the standard deviation is 5 minutes.
Find the probability that a student, chosen at random arrives at least 60 minutes after the school opens.
Find the probability that a student, chosen at random arrives between 45 minutes and 55 minutes after the school opens.
A second school, Mulberry Park, also opens at 08:00 every morning. The arrival times of the students at this school follows exactly the same distribution as Malthouse school.
Given that, on one morning, 15 students arrive at least 60 minutes after the school opens, estimate the number of students at Mulberry Park school.
Markscheme
0.0548 (0.054799…, 5.48%) (A2) (C2)
[2 marks]
0.645 (0.6449900…, 64.5%) (A2) (C2)
[2 marks]
\(\frac{{15}}{{0.0548}}\) (M1)
Note: Award (M1) for dividing 15 by their part (a)(i).
Accept an equation of the form 15 = x × 0.0548 for (M1).
274 (273.722…) (A1)(ft) (C2)
Note: Follow through from part (a)(i). Accept 273.
[2 marks]
