Ages Number of students 15-18 3 19-22 23-26 10 27-30 7 31-34 35-38 Based on the frequency distribution above, find the relative frequency for the class with lower class limit 31 Relative Frequency % Give your answer as a percent, rounded to one decimal place
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![### Frequency Distribution Table
The table below shows the frequency distribution of students across different age groups:
| Ages | Number of students |
|-------|--------------------|
| 15-18 | 3 |
| 19-22 | 5 |
| 23-26 | 10 |
| 27-30 | 7 |
| 31-34 | 2 |
| 35-38 | 5 |
### Problem Statement
Based on the frequency distribution above, find the relative frequency for the class with the lower class limit of 31.
- **Relative Frequency Calculation**: Relative Frequency = \( \frac{\text{Frequency of the class}}{\text{Total number of students}} \times 100 \)
- **Total number of students**: Sum all the frequencies in the table.
### Calculation
1. **Total Number of Students**:
\[ \text{Total students} = 3 + 5 + 10 + 7 + 2 + 5 = 32 \]
2. **Frequency for the class with lower class limit 31**:
Frequency for age group 31-34 = 2
3. **Relative Frequency**:
\[
\text{Relative Frequency} = \left(\frac{2}{32}\right) \times 100
\]
4. **Result**:
\[
\text{Relative Frequency} = \left(\frac{2}{32}\right) \times 100 = 6.25\%
\]
So, the relative frequency for the class with the lower class limit of 31 is \( 6.3\% \).
Please input this value into the box below:
**Relative Frequency** = \( \boxed{6.3} \)%
(Note: Decimal is rounded to one decimal place as instructed)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F443e45af-3927-4fd9-baca-290567a407b3%2Ff2753136-c542-48ad-b268-c9f02264d155%2Fbjxclj_processed.png&w=3840&q=75)
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