Intermediate June 2024 Unit 1 Q5
5. In a game, each competitor will have 20 attempts at throwing a ball into a bucket.
They will get 1 point for every ball that lands in the bucket.
Sioned wants to keep a record of the total points for each competitor.
She decides to show the results in a table with the total points recorded in groups of equal width.
(a) She starts to draw a table using five groups, as shown below.
Explain why these groups will not be suitable. [1]
| Total points | 0 to 3 | 4 to 7 | 8 to 11 | … to … | … to … |
|---|---|---|---|---|---|
| Number of competitors |
(b) Sioned considers using the table shown below.
She decides that it is suitable for recording all the total points in groups of equal width.
Fill in the two missing numbers in the top row. [1]
She decides that it is suitable for recording all the total points in groups of equal width.
Fill in the two missing numbers in the top row. [1]
| Total points | 0 to 6 | 7 to ………… | ………… to 20 |
|---|---|---|---|
| Number of competitors |
(c) Finally, Sioned decides to use the groups shown in the table below.
The results for the first 100 competitors are shown in the table.
The results for the first 100 competitors are shown in the table.
| Total points | 0 to 2 | 3 to 5 | 6 to 8 | 9 to 11 | 12 to 14 | 15 to 17 | 18 to 20 |
|---|---|---|---|---|---|---|---|
| Number of competitors | 5 | 10 | 17 | 22 | 23 | 12 | 11 |
One of these 100 competitors is chosen at random.
(i) What is the probability that this competitor scored 6, 7 or 8 points? [1]
(ii) Explain why the following statement may be incorrect. [1]
The probability that this competitor scored 19 points is \(\dfrac{11}{100}\).
| Scheme | Marks | Comments |
|---|---|---|
| A correct explanation given. e.g. ‘(equal) groups do not reach 20’, ‘12 to 15 and 16 to 19 so no 20’, ‘ to reach 20 the groups are not equal’ ‘it only goes up to 19’ ‘20 not included’. | E1 | Allow any unambiguous explanation. Do not accept: ‘because there’s only 20 attempts’. Award E1 if incorrect values are given in the table but correct explanation given. |
| Scheme | Marks | Comments |
|---|---|---|
| (0 to 6) 7 to 13 14 to 20 | B1 | Answer in table takes precedence. |
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(\dfrac{17}{100}\) or equivalent ISW | B1 | B0 for incorrect notation e.g. ’17 in 100’, ’17 out of 100’, ’17:100’ etc. |
| (ii) A correct explanation given e.g. ‘the eleven competitors might have all scored 20’, ‘only one of them (might have) scored 19’, ‘we don’t know how many competitors scored 19’ ‘the probability of scoring 18, 19 or 20 is \(\dfrac{11}{100}\) ’ ‘the 11 could include (the scores of) 18 and 20’ ‘it doesn’t tell you the exact score of all 11 competitors’ | E1 | Allow any unambiguous explanation. E0 for mixing number of competitors and number of points scored. e.g. ‘11 points were scored for 18, 19, 20’ ‘18, 19 or 20 people could have scored 11’. |