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An animal shelter takes cats and dogs - Leaving Cert Mathematics - Question 7 - 2022
Question 7
An animal shelter takes cats and dogs. The staff record the weight of each animal in the shelter on two different days: the day they are taken in to the shelter (Da... show full transcript
Worked Solution & Example Answer:An animal shelter takes cats and dogs - Leaving Cert Mathematics - Question 7 - 2022
Step 1
Draw a back-to-back stem-and-leaf plot to show this information.
Answer
To create a back-to-back stem-and-leaf plot, we first need to group the weights of the dogs based on their values. The stems will be the leading digits, while the leaves will represent the last digits.
For Day X:
- 4 | 5
- 5 | 3, 5, 7
- 6 | 0, 7, 9
- 7 | 3, 4
For Day Y:
- 4 | 8
- 5 | 4, 5
- 6 | 0, 1, 3
- 7 | 6, 9
- 8 | 1, 9
The back-to-back plot shows the distribution of weights for both days clearly, allowing us to compare them visually.
Step 2
What does the stem-and-leaf plot show about the weights of the dogs on Day X and Day Y?
Answer
The stem-and-leaf plot indicates that the weights of the dogs have generally increased from Day X to Day Y. On Day X, the weights cluster around lower values (ranging from 4.5 kg to 7.4 kg), while on Day Y, the weights are slightly higher (from 4.8 kg to 8.1 kg). This suggests that the dogs may have gained weight over the period.
Step 3
r is the correlation coefficient between the weight on Day X and the weight on Day Y. Based on the data in the table, pick the most likely value of r from the list below.
Answer
is likely to be . This high positive value suggests a strong correlation between the weights on Day X and Day Y, indicating that as one weight increases, the other weight also tends to increase.
Step 4
Complete the table, by filling in the four missing values.
Answer
To complete the table:
- Total number of cats is 14.
- Total number of dogs is given as 11, so Total = 30 - 14 = 16 dogs.
- Total animals = 40, thus the combined total is 40, hence the four missing values are:
| Male | Female | Total | |
|---|---|---|---|
| Cats | 5 | 9 | 14 |
| Dogs | 11 | 5 | 16 |
| Total | 16 | 24 | 40 |
Step 5
Step 6
Step 7
Work out the number of ways in which this could have been done.
Answer
The number of different possible arrangements of 9 female cats in 9 separate pens is calculated using the factorial formula:
Therefore, there are 362880 different arrangements in which the 9 female cats could be placed into the pens.
Step 8
Work out how many cats left the shelter during this week.
Answer
Initially, there were 40 animals in total. By the end of the week, 10 animals had left the shelter. If the probability of picking a dog is (\frac{11}{15}), we calculate the number of remaining dogs:
Hence, originally there were 22 cats, and 6 cats must have left the shelter during this week.