4MA0 Foundation June 2014 Paper 1R Q16
16 Freya keeps hens.
The table shows information about the number of boxes of eggs she sold in each of 52 weeks.
| Number of boxes sold in a week | Number of weeks |
|---|---|
| 0 to 4 | 2 |
| 5 to 9 | 6 |
| 10 to 14 | 20 |
| 15 to 19 | 13 |
| 20 to 24 | 8 |
| 25 to 29 | 3 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean number of boxes of eggs that Freya sold each week.
Give your answer correct to 3 significant figures. (4)
Give your answer correct to 3 significant figures. (4)
Dan picks at random one of the 52 weeks.
(c) Find the probability that in this week Freya sold at least 15 boxes of eggs. (2)
| Scheme | Marks |
|---|---|
| 10 to 14 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 2 × 2 + 6 × 7 + 20 × 12 + 13 × 17 + 8 × 22 + 3 × 27 or 4 + 42 + 240 + 221 + 176 + 81 or 764 | M2 |
| “764” ÷ 52 | M1 |
| 14.7 | A1 |
| (4) |
Notes
M2: Freq × all correct midpoint values stated or evaluated with intention to add (condone any one error). If not M2 then award M1 for all products \(t \times f\) (and \(t\) is consistently within the interval, including end values) and intention to add (condone any one error)
M1: (dep on at least M1) for division by 52.
Accept their 52 if addition shown.
A1: for answer rounding to 14.7
Accept 15 with working (15 without working gains NO marks).
| Scheme | Marks |
|---|---|
| \(\dfrac{13 + 8 + 3}{52}\) | M1 |
| \(\dfrac{24}{52}\) \(\dfrac{6}{13}\) oe | A1 |
| (2) | |
| (Total 7 marks) |
Notes
M1: for 13 + 8 + 3 or 24 or \(\dfrac{a}{52}\) where \(a < 52\)
A1: Accept 0.46… (at least 2DP)