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.
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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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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