Problem 2) Agriculture officials placed sticky traps in fruit trees at random throughout a neighborhood. They collected the traps and counted the number of fruit flies per trap. The data appear below: Fruit Flies in Sticky Traps Number of fruit Number of flies per trap traps 32 1 35 33 3 9. 4 Compute the mean а. 1.23 2 5 b. 1.42 с. 1.32 d. 1.39 Compute the standard deviation а. 1.23 b. 1.42 с. 1.32 1. 20

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### Problem 2: Analysis of Fruit Fly Distribution in Traps

Agriculture officials placed sticky traps in fruit trees at random throughout a neighborhood. They collected the traps and counted the number of fruit flies per trap. The data appear below:

#### Fruit Flies in Sticky Traps
| Number of fruit flies per trap | Number of traps |
|--------------------------------|-----------------|
| 0                              | 32              |
| 1                              | 35              |
| 2                              | 33              |
| 3                              | 9               |
| 4                              | 5               |
| ≥ 5                            | 3               |

1. **Compute the mean:**
    - Options:
        a. 1.23
        b. 1.42
        c. 1.32
        d. 1.39
      
2. **Compute the standard deviation:**
    - Options:
        a. 1.23
        b. 1.42
        c. 1.32
        d. 1.39

#### Continuation of Problem 2

If fruit flies are randomly distributed throughout the neighborhood, then the number of fruit flies per trap should follow a Poisson distribution. Use the sample mean and the Poisson probability distribution to obtain probabilities (carry four decimal places) and expected frequencies (to one decimal place) for these data.

3. **Compute the expected frequency based on Poisson distribution for \( K = 0 \):**
    - Options:
        a. 28.2
        b. 40.5
        c. 33.0
        d. 29.0
      
4. **Compute the expected frequency based on Poisson distribution for \( K = 1 \):**
    - Options:
        a. 28.2
        b. 40.5
        c. 33.0
        d. 29.0
      
5. **Compute the expected frequency based on Poisson distribution for \( K = 2 \):**
    - Options:
        a. 28.2
        b. 40.5
        c. 33.0
        d. 29.0

6. **Compute the expected frequency based on Poisson distribution for \( K \geq 5 \):**
    - Options:
        a. 2.6
        b. 2.3
        c
Transcribed Image Text:### Problem 2: Analysis of Fruit Fly Distribution in Traps Agriculture officials placed sticky traps in fruit trees at random throughout a neighborhood. They collected the traps and counted the number of fruit flies per trap. The data appear below: #### Fruit Flies in Sticky Traps | Number of fruit flies per trap | Number of traps | |--------------------------------|-----------------| | 0 | 32 | | 1 | 35 | | 2 | 33 | | 3 | 9 | | 4 | 5 | | ≥ 5 | 3 | 1. **Compute the mean:** - Options: a. 1.23 b. 1.42 c. 1.32 d. 1.39 2. **Compute the standard deviation:** - Options: a. 1.23 b. 1.42 c. 1.32 d. 1.39 #### Continuation of Problem 2 If fruit flies are randomly distributed throughout the neighborhood, then the number of fruit flies per trap should follow a Poisson distribution. Use the sample mean and the Poisson probability distribution to obtain probabilities (carry four decimal places) and expected frequencies (to one decimal place) for these data. 3. **Compute the expected frequency based on Poisson distribution for \( K = 0 \):** - Options: a. 28.2 b. 40.5 c. 33.0 d. 29.0 4. **Compute the expected frequency based on Poisson distribution for \( K = 1 \):** - Options: a. 28.2 b. 40.5 c. 33.0 d. 29.0 5. **Compute the expected frequency based on Poisson distribution for \( K = 2 \):** - Options: a. 28.2 b. 40.5 c. 33.0 d. 29.0 6. **Compute the expected frequency based on Poisson distribution for \( K \geq 5 \):** - Options: a. 2.6 b. 2.3 c
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