Question

problem solving the heart rates (in beats per minute) for a random sample of 36 blue whales are shown in the table.
blue whale heart rates
11 10 12 12 8 10
13 11 13 9 11 8
12 6 8 13 5 8
9 8 12 6 9 7
6 8 7 9 9 5
12 9 11 7 8 9
a. estimate the population proportion of blue whales that have a heart rate greater than 10 beats per minute.
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b. estimate the population proportion of blue whales that have a heart rate less than 8 beats per minute.
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Explanation:

Step1: Solve part (a)

First, we need to count the number of blue whales with heart rate greater than 10. Let's list the data:

The heart rates are: 11, 10, 12, 12, 8, 10, 13, 11, 13, 9, 11, 8, 12, 6, 8, 13, 5, 8, 9, 8, 12, 6, 9, 7, 6, 8, 7, 9, 9, 5, 12, 9, 11, 7, 8, 9.

Now, identify values > 10: 11, 12, 12, 13, 11, 13, 11, 12, 13, 12, 11, 12. Let's count them:

1. 11 (1)
2. 12 (2)
3. 12 (3)
4. 13 (4)
5. 11 (5)
6. 13 (6)
7. 11 (7)
8. 12 (8)
9. 13 (9)
10. 12 (10)
11. 11 (11)
12. 12 (12)

Wait, let's do it more carefully. Let's go through each number:

Row 1: 11 (1), 10 (no), 12 (2), 12 (3), 8 (no), 10 (no) → 3
Row 2: 13 (4), 11 (5), 13 (6), 9 (no), 11 (7), 8 (no) → 3 (total 6)
Row 3: 12 (8), 6 (no), 8 (no), 13 (9), 5 (no), 8 (no) → 2 (total 8)
Row 4: 9 (no), 8 (no), 12 (10), 6 (no), 9 (no), 7 (no) → 1 (total 9)
Row 5: 6 (no), 8 (no), 7 (no), 9 (no), 9 (no), 5 (no) → 0 (total 9)
Row 6: 12 (11), 9 (no), 11 (12), 7 (no), 8 (no), 9 (no) → 2 (total 12)

Wait, maybe a better way: count all numbers >10. The numbers >10 are 11, 12, 13.

Let's list all values and count:

11 appears: let's see, positions 1, 8, 11, 34 → 4 times? Wait, no, let's list all:

1. 11
2. 10
3. 12
4. 12
5. 8
6. 10
7. 13
8. 11
9. 13
10. 9
11. 11
12. 8
13. 12
14. 6
15. 8
16. 13
17. 5
18. 8
19. 9
20. 8
21. 12
22. 6
23. 9
24. 7
25. 6
26. 8
27. 7
28. 9
29. 9
30. 5
31. 12
32. 9
33. 11
34. 7
35. 8
36. 9

Now, count values >10:

11: positions 1, 8, 11, 33 → 4
12: positions 3, 4, 13, 21, 31 → 5
13: positions 7, 9, 16 → 3
Total: 4 + 5 + 3 = 12

Total sample size n = 36.

So the proportion is $\frac{12}{36} = \frac{1}{3} \approx 0.333$.

Step2: Solve part (b)

Now, count the number of heart rates less than 8. Values less than 8 are 5, 6, 7.

Let's list the data and count:

5: positions 17, 30 → 2
6: positions 14, 22, 25 → 3
7: positions 24, 27, 34 → 3
Total: 2 + 3 + 3 = 8

Proportion is $\frac{8}{36} = \frac{2}{9} \approx 0.222$.

Answer:

a. About $\frac{1}{3}$ (or 0.333)
b. About $\frac{2}{9}$ (or 0.222)