Jenny recorded the time, in minutes, of 40 movies. The table summarises her results. Time (t minutes) | 60<t≤80 | 80<t≤100 | 100<t≤120 | 120<t≤140 | 140 <t≤ 160 Frequency | 2 | 7 | 15 | 11 | 5 Jenny asked 60 people how many movies they had each watched in the last month. The table summarises her results. Number of movies | 0 | 1 | 2 | 3 | 4 | 5 | 6 Frequency | p | 14 | 15 | 7 | q | 5 | 2 The mean number of movies watched is 2.3. Jenny also asked which type of movie each of the 60 people preferred. The table summarises her results. Type of movie | Action | Comedy | Drama | Horror Frequency | 24 | 15 | 9 | 12
- (a)On the grid, draw a frequency polygon to represent this information. [Figure: grid with axes Time (t minutes) and Frequency, scaled 0-160 and 0-16 respectively][2]
- (b)Find the value of p and the value of q.[3]
- (c)(i)Complete the pie chart to represent the results. [Figure: incomplete pie chart with 'Action' sector drawn][3]
- (c)(ii)One of the 60 people is chosen at random. Find the probability that this person preferred drama or horror movies.[1]
- (c)(iii)Two of the 60 people are chosen at random. Calculate the probability that they both preferred comedy movies.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [2] B1 for 4 or 5 heights correct soi
- [3] B2 M1 for [0×p] + 1×14+2×15 + 3×7 + 4×q + 5×5 + 6×2 oe
- B1 Strict FT provided q integer with 0 <q ≤ 17
- [3] B2 for correct sectors without labels or incorrect labels or B1 for one correct sector or 90, 54 and 72 seen
- [1] 21/60, 7/20, 0.35 or 35%
- [2] M1 for 15/60 * 14/59 [oe] or SC1 for 15/60 * 15/60 or answer 1/16 oe
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