An empirical probability distribution based on weekly study times for a sample of 40 students is provided to the right. Suppose one of those students was chosen randomly. In parts (a) through (d) below, using your distribution, find the probability that the study time in the past week for the student selected would have been in each of the following ranges. Class Limits Frequency Relative f Frequency 10-19 0.150 .... 20-29 11 0.275 (a) 30-39 hours 30-39 1 0.025 (Type an integer or a decimal.) 40-49 15 0.375 50-59 0.050 (b) 40-59 hours 60-69 0.025 (Type an integer or a decimal.) 70-79 4. 0.100 Total: n= 40 (c) fewer than 30 hours (Type an integer or a decimal.) (d) at least 50 hours (Type an integer or a decimal.)
An empirical probability distribution based on weekly study times for a sample of 40 students is provided to the right. Suppose one of those students was chosen randomly. In parts (a) through (d) below, using your distribution, find the probability that the study time in the past week for the student selected would have been in each of the following ranges. Class Limits Frequency Relative f Frequency 10-19 0.150 .... 20-29 11 0.275 (a) 30-39 hours 30-39 1 0.025 (Type an integer or a decimal.) 40-49 15 0.375 50-59 0.050 (b) 40-59 hours 60-69 0.025 (Type an integer or a decimal.) 70-79 4. 0.100 Total: n= 40 (c) fewer than 30 hours (Type an integer or a decimal.) (d) at least 50 hours (Type an integer or a decimal.)
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![### Empirical Probability Distribution of Weekly Study Times
This educational exercise involves analyzing an empirical probability distribution of study times over the past week for a sample of 40 students. The frequency distribution data is provided in a table format.
#### Frequency Distribution Table:
| Class Limits (hours) | Frequency (f) | Relative Frequency |
|----------------------|---------------|--------------------|
| 10-19 | 6 | 0.150 |
| 20-29 | 11 | 0.275 |
| 30-39 | 1 | 0.025 |
| 40-49 | 15 | 0.375 |
| 50-59 | 2 | 0.050 |
| 60-69 | 1 | 0.025 |
| 70-79 | 4 | 0.100 |
| **Total** | **n = 40** | |
### Exercises:
Using the distribution above, find the probability that a randomly selected student studied for the indicated range of hours.
#### (a) Probability for 30-39 hours:
\[ \text{Probability} = 0.025 \]
#### (b) Probability for 40-59 hours:
Add the relative frequencies for the 40-49 hours and 50-59 hours ranges:
\[ \text{Probability} = 0.375 + 0.050 = 0.425 \]
#### (c) Probability for fewer than 30 hours:
Add the relative frequencies for the 10-19 hours and 20-29 hours ranges:
\[ \text{Probability} = 0.150 + 0.275 = 0.425 \]
#### (d) Probability for at least 50 hours:
Add the relative frequencies for the 50-59 hours, 60-69 hours, and 70-79 hours ranges:
\[ \text{Probability} = 0.050 + 0.025 + 0.100 = 0.175 \]
These exercises provide practice in calculating probabilities from a frequency distribution, enhancing understanding of empirical probability in a real-world context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ce5d754-3f10-4df1-a7fc-056de649c4d6%2Fef735310-c340-4890-88bb-7e754b3ebb78%2F32bn1h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Empirical Probability Distribution of Weekly Study Times
This educational exercise involves analyzing an empirical probability distribution of study times over the past week for a sample of 40 students. The frequency distribution data is provided in a table format.
#### Frequency Distribution Table:
| Class Limits (hours) | Frequency (f) | Relative Frequency |
|----------------------|---------------|--------------------|
| 10-19 | 6 | 0.150 |
| 20-29 | 11 | 0.275 |
| 30-39 | 1 | 0.025 |
| 40-49 | 15 | 0.375 |
| 50-59 | 2 | 0.050 |
| 60-69 | 1 | 0.025 |
| 70-79 | 4 | 0.100 |
| **Total** | **n = 40** | |
### Exercises:
Using the distribution above, find the probability that a randomly selected student studied for the indicated range of hours.
#### (a) Probability for 30-39 hours:
\[ \text{Probability} = 0.025 \]
#### (b) Probability for 40-59 hours:
Add the relative frequencies for the 40-49 hours and 50-59 hours ranges:
\[ \text{Probability} = 0.375 + 0.050 = 0.425 \]
#### (c) Probability for fewer than 30 hours:
Add the relative frequencies for the 10-19 hours and 20-29 hours ranges:
\[ \text{Probability} = 0.150 + 0.275 = 0.425 \]
#### (d) Probability for at least 50 hours:
Add the relative frequencies for the 50-59 hours, 60-69 hours, and 70-79 hours ranges:
\[ \text{Probability} = 0.050 + 0.025 + 0.100 = 0.175 \]
These exercises provide practice in calculating probabilities from a frequency distribution, enhancing understanding of empirical probability in a real-world context.
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