Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data: 2 1 4 1 3 2 3 3 1 3 4 7 3 4 2 1 3 1 1 3 4 1 2 3 2 8. 4 1 1 3 1 6. 4 2 1 6. 3 3 6. 1 3 Determine frequencies and relative frequencies for the observed values of nonconforming transducers in a batch. b. What proportion of batches in the sample have at most five nonconforming transducers? What proportion have fewer than five? What proportion have at least five nonconforming а. units? Draw a histogram of the data using relative frequency on the vertical scale, and comment on its features. с.

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### Problem 2: Analysis of Temperature Transducer Batches

Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:

```
2, 1, 2, 4, 0, 1, 3, 2, 0, 5, 3, 3, 
1, 3, 2, 4, 7, 0, 2, 3, 0, 4, 2, 1, 
3, 1, 1, 3, 4, 1, 2, 3, 2, 2, 8, 4, 
5, 1, 3, 1, 5, 0, 2, 3, 2, 1, 0, 6, 
4, 2, 1, 6, 0, 3, 3, 3, 6, 1, 2, 3
```

**Tasks:**

a. **Determine frequencies and relative frequencies for the observed values of nonconforming transducers in a batch.**

b. **What proportion of batches in the sample have at most five nonconforming transducers? What proportion have fewer than five? What proportion have at least five nonconforming units?**

c. **Draw a histogram of the data using relative frequency on the vertical scale, and comment on its features.**

### Explanation

For each task, follow these steps:

a. **Frequencies and Relative Frequencies:**
   - Tally the occurrences of each number of nonconforming transducers.
   - Calculate the relative frequency by dividing each frequency by the total number of batches (60).

b. **Proportions:**
   - Calculate the proportion of batches with at most five, fewer than five, and at least five nonconforming units.

c. **Histogram:**
   - Create a histogram with the number of nonconforming transducers on the horizontal axis and relative frequency on the vertical axis.
   - Observe patterns such as skewness, peaks, or uniform distribution.
Transcribed Image Text:### Problem 2: Analysis of Temperature Transducer Batches Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data: ``` 2, 1, 2, 4, 0, 1, 3, 2, 0, 5, 3, 3, 1, 3, 2, 4, 7, 0, 2, 3, 0, 4, 2, 1, 3, 1, 1, 3, 4, 1, 2, 3, 2, 2, 8, 4, 5, 1, 3, 1, 5, 0, 2, 3, 2, 1, 0, 6, 4, 2, 1, 6, 0, 3, 3, 3, 6, 1, 2, 3 ``` **Tasks:** a. **Determine frequencies and relative frequencies for the observed values of nonconforming transducers in a batch.** b. **What proportion of batches in the sample have at most five nonconforming transducers? What proportion have fewer than five? What proportion have at least five nonconforming units?** c. **Draw a histogram of the data using relative frequency on the vertical scale, and comment on its features.** ### Explanation For each task, follow these steps: a. **Frequencies and Relative Frequencies:** - Tally the occurrences of each number of nonconforming transducers. - Calculate the relative frequency by dividing each frequency by the total number of batches (60). b. **Proportions:** - Calculate the proportion of batches with at most five, fewer than five, and at least five nonconforming units. c. **Histogram:** - Create a histogram with the number of nonconforming transducers on the horizontal axis and relative frequency on the vertical axis. - Observe patterns such as skewness, peaks, or uniform distribution.
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