| Date | May 2018 | Marks available | 3 | Reference code | 18M.1.sl.TZ2.12 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Calculate | Question number | 12 | Adapted from | N/A |
Question
The histogram shows the time, t, in minutes, that it takes the customers of a restaurant to eat their lunch on one particular day. Each customer took less than 25 minutes.
The histogram is incomplete, and only shows data for 0 ≤ t < 20.
The mean time it took all customers to eat their lunch was estimated to be 12 minutes.
It was found that k customers took between 20 and 25 minutes to eat their lunch.
Write down the mid-interval value for 10 ≤ t < 15.
Write down the total number of customers in terms of k.
Calculate the value of k.
Hence, complete the histogram.
Markscheme
12.5 (A1) (C1)
[1 mark]
33 + k OR 10 + 8 + 5 + 10 + k (A1)
Note: Award (A1) for “number of customers = 33 + k”.
[1 mark]
\(\frac{{2.5 \times 10 + 7.5 \times 8 + \ldots + 22.5 \times k}}{{33 + k}} = 12\) (M1)(A1)(ft)
Note: Award (M1) for substitution into the mean formula and equating to 12, (A1)(ft) for their correct substitutions.
(k =) 7 (A1)(ft) (C4)
Note: Follow through from part (b)(i) and their mid-interval values, consistent with part (a). Do not award final (A1) if answer is not an integer.
[3 marks]
(A1)(ft) (C1)
Note: Follow through from their part (b)(ii) but only if the value is between 1 and 10, inclusive.
[1 mark]
