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Sagot :
Let's proceed step-by-step to analyze the data from the experiment conducted by Lee. The goal is to determine the maze times for fish before and after exposure to the special microwaved food and to assess the improvement.
### Step 1: Convert Time Data to Seconds
First, we need to convert the maze times from minutes and seconds into total seconds for easier calculations.
#### Before Eating Special Food:
1. Fish 1: 1 minute 6 seconds = [tex]\( 1 \times 60 + 6 = 66 \)[/tex] seconds
2. Fish 2: 1 minute 54 seconds = [tex]\( 1 \times 60 + 54 = 114 \)[/tex] seconds
3. Fish 3: 2 minutes 4 seconds = [tex]\( 2 \times 60 + 4 = 124 \)[/tex] seconds
4. Fish 4: 2 minutes 15 seconds = [tex]\( 2 \times 60 + 15 = 135 \)[/tex] seconds
5. Fish 5: 1 minute 27 seconds = [tex]\( 1 \times 60 + 27 = 87 \)[/tex] seconds
6. Fish 6: 1 minute 45 seconds = [tex]\( 1 \times 60 + 45 = 105 \)[/tex] seconds
7. Fish 7: 1 minute 0 seconds = [tex]\( 1 \times 60 + 0 = 60 \)[/tex] seconds
8. Fish 8: 1 minute 28 seconds = [tex]\( 1 \times 60 + 28 = 88 \)[/tex] seconds
9. Fish 9: 1 minute 9 seconds = [tex]\( 1 \times 60 + 9 = 69 \)[/tex] seconds
10. Fish 10: 2 minutes 0 seconds = [tex]\( 2 \times 60 + 0 = 120 \)[/tex] seconds
#### After Eating Special Food:
1. Fish 1: 1 minute 0 seconds = [tex]\( 1 \times 60 + 0 = 60 \)[/tex] seconds
2. Fish 2: 1 minute 20 seconds = [tex]\( 1 \times 60 + 20 = 80 \)[/tex] seconds
3. Fish 3: 1 minute 57 seconds = [tex]\( 1 \times 60 + 57 = 117 \)[/tex] seconds
4. Fish 4: 2 minutes 20 seconds = [tex]\( 2 \times 60 + 20 = 140 \)[/tex] seconds
5. Fish 5: 1 minute 20 seconds = [tex]\( 1 \times 60 + 20 = 80 \)[/tex] seconds
6. Fish 6: 1 minute 40 seconds = [tex]\( 1 \times 60 + 40 = 100 \)[/tex] seconds
7. Fish 7: 1 minute 15 seconds = [tex]\( 1 \times 60 + 15 = 75 \)[/tex] seconds
8. Fish 8: 1 minute 26 seconds = [tex]\( 1 \times 60 + 26 = 86 \)[/tex] seconds
9. Fish 9: 1 minute 0 seconds = [tex]\( 1 \times 60 + 0 = 60 \)[/tex] seconds
10. Fish 10: 1 minute 43 seconds = [tex]\( 1 \times 60 + 43 = 103 \)[/tex] seconds
### Step 2: Calculate Total and Average Times
Next, we calculate the total and average times for the fish before and after eating the special food.
#### Total Times:
- Before:
[tex]\[ 66 + 114 + 124 + 135 + 87 + 105 + 60 + 88 + 69 + 120 = 968 \text{ seconds} \][/tex]
- After:
[tex]\[ 60 + 80 + 117 + 140 + 80 + 100 + 75 + 86 + 60 + 103 = 901 \text{ seconds} \][/tex]
#### Average Times:
- Before:
[tex]\[ \frac{968}{10} = 96.8 \text{ seconds} \][/tex]
- After:
[tex]\[ \frac{901}{10} = 90.1 \text{ seconds} \][/tex]
### Step 3: Calculate Improvement
Now we calculate the improvement for each fish, then find the total and average improvement.
#### Individual Improvements:
- Fish 1: [tex]\( 66 - 60 = 6 \)[/tex] seconds
- Fish 2: [tex]\( 114 - 80 = 34 \)[/tex] seconds
- Fish 3: [tex]\( 124 - 117 = 7 \)[/tex] seconds
- Fish 4: [tex]\( 135 - 140 = -5 \)[/tex] seconds (negative indicates no improvement)
- Fish 5: [tex]\( 87 - 80 = 7 \)[/tex] seconds
- Fish 6: [tex]\( 105 - 100 = 5 \)[/tex] seconds
- Fish 7: [tex]\( 60 - 75 = -15 \)[/tex] seconds (negative indicates no improvement)
- Fish 8: [tex]\( 88 - 86 = 2 \)[/tex] seconds
- Fish 9: [tex]\( 69 - 60 = 9 \)[/tex] seconds
- Fish 10: [tex]\( 120 - 103 = 17 \)[/tex] seconds
#### Total Improvement:
[tex]\[ 6 + 34 + 7 - 5 + 7 + 5 - 15 + 2 + 9 + 17 = 67 \text{ seconds} \][/tex]
#### Average Improvement:
[tex]\[ \frac{67}{10} = 6.7 \text{ seconds} \][/tex]
### Summary
- Total time before special food: 968 seconds
- Total time after special food: 901 seconds
- Average time before special food: 96.8 seconds
- Average time after special food: 90.1 seconds
- Total improvement: 67 seconds
- Average improvement per fish: 6.7 seconds
These results suggest that the special microwaved food helped the fish improve their maze completion times on average, though not all individuals showed improvement.
### Step 1: Convert Time Data to Seconds
First, we need to convert the maze times from minutes and seconds into total seconds for easier calculations.
#### Before Eating Special Food:
1. Fish 1: 1 minute 6 seconds = [tex]\( 1 \times 60 + 6 = 66 \)[/tex] seconds
2. Fish 2: 1 minute 54 seconds = [tex]\( 1 \times 60 + 54 = 114 \)[/tex] seconds
3. Fish 3: 2 minutes 4 seconds = [tex]\( 2 \times 60 + 4 = 124 \)[/tex] seconds
4. Fish 4: 2 minutes 15 seconds = [tex]\( 2 \times 60 + 15 = 135 \)[/tex] seconds
5. Fish 5: 1 minute 27 seconds = [tex]\( 1 \times 60 + 27 = 87 \)[/tex] seconds
6. Fish 6: 1 minute 45 seconds = [tex]\( 1 \times 60 + 45 = 105 \)[/tex] seconds
7. Fish 7: 1 minute 0 seconds = [tex]\( 1 \times 60 + 0 = 60 \)[/tex] seconds
8. Fish 8: 1 minute 28 seconds = [tex]\( 1 \times 60 + 28 = 88 \)[/tex] seconds
9. Fish 9: 1 minute 9 seconds = [tex]\( 1 \times 60 + 9 = 69 \)[/tex] seconds
10. Fish 10: 2 minutes 0 seconds = [tex]\( 2 \times 60 + 0 = 120 \)[/tex] seconds
#### After Eating Special Food:
1. Fish 1: 1 minute 0 seconds = [tex]\( 1 \times 60 + 0 = 60 \)[/tex] seconds
2. Fish 2: 1 minute 20 seconds = [tex]\( 1 \times 60 + 20 = 80 \)[/tex] seconds
3. Fish 3: 1 minute 57 seconds = [tex]\( 1 \times 60 + 57 = 117 \)[/tex] seconds
4. Fish 4: 2 minutes 20 seconds = [tex]\( 2 \times 60 + 20 = 140 \)[/tex] seconds
5. Fish 5: 1 minute 20 seconds = [tex]\( 1 \times 60 + 20 = 80 \)[/tex] seconds
6. Fish 6: 1 minute 40 seconds = [tex]\( 1 \times 60 + 40 = 100 \)[/tex] seconds
7. Fish 7: 1 minute 15 seconds = [tex]\( 1 \times 60 + 15 = 75 \)[/tex] seconds
8. Fish 8: 1 minute 26 seconds = [tex]\( 1 \times 60 + 26 = 86 \)[/tex] seconds
9. Fish 9: 1 minute 0 seconds = [tex]\( 1 \times 60 + 0 = 60 \)[/tex] seconds
10. Fish 10: 1 minute 43 seconds = [tex]\( 1 \times 60 + 43 = 103 \)[/tex] seconds
### Step 2: Calculate Total and Average Times
Next, we calculate the total and average times for the fish before and after eating the special food.
#### Total Times:
- Before:
[tex]\[ 66 + 114 + 124 + 135 + 87 + 105 + 60 + 88 + 69 + 120 = 968 \text{ seconds} \][/tex]
- After:
[tex]\[ 60 + 80 + 117 + 140 + 80 + 100 + 75 + 86 + 60 + 103 = 901 \text{ seconds} \][/tex]
#### Average Times:
- Before:
[tex]\[ \frac{968}{10} = 96.8 \text{ seconds} \][/tex]
- After:
[tex]\[ \frac{901}{10} = 90.1 \text{ seconds} \][/tex]
### Step 3: Calculate Improvement
Now we calculate the improvement for each fish, then find the total and average improvement.
#### Individual Improvements:
- Fish 1: [tex]\( 66 - 60 = 6 \)[/tex] seconds
- Fish 2: [tex]\( 114 - 80 = 34 \)[/tex] seconds
- Fish 3: [tex]\( 124 - 117 = 7 \)[/tex] seconds
- Fish 4: [tex]\( 135 - 140 = -5 \)[/tex] seconds (negative indicates no improvement)
- Fish 5: [tex]\( 87 - 80 = 7 \)[/tex] seconds
- Fish 6: [tex]\( 105 - 100 = 5 \)[/tex] seconds
- Fish 7: [tex]\( 60 - 75 = -15 \)[/tex] seconds (negative indicates no improvement)
- Fish 8: [tex]\( 88 - 86 = 2 \)[/tex] seconds
- Fish 9: [tex]\( 69 - 60 = 9 \)[/tex] seconds
- Fish 10: [tex]\( 120 - 103 = 17 \)[/tex] seconds
#### Total Improvement:
[tex]\[ 6 + 34 + 7 - 5 + 7 + 5 - 15 + 2 + 9 + 17 = 67 \text{ seconds} \][/tex]
#### Average Improvement:
[tex]\[ \frac{67}{10} = 6.7 \text{ seconds} \][/tex]
### Summary
- Total time before special food: 968 seconds
- Total time after special food: 901 seconds
- Average time before special food: 96.8 seconds
- Average time after special food: 90.1 seconds
- Total improvement: 67 seconds
- Average improvement per fish: 6.7 seconds
These results suggest that the special microwaved food helped the fish improve their maze completion times on average, though not all individuals showed improvement.
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