Sally decides to do an experiment to see how many times her MP3 player will shuffle through her songs and play her favorite group, "The Googly Girls" per hour. Her results are shown in the probability distribution table below. Find the expected value that the MP3 player will a song by "The Googly Girls" each hour. 1 p(x) 0.23 0.36 0.27 0.14
Sally decides to do an experiment to see how many times her MP3 player will shuffle through her songs and play her favorite group, "The Googly Girls" per hour. Her results are shown in the probability distribution table below. Find the expected value that the MP3 player will a song by "The Googly Girls" each hour. 1 p(x) 0.23 0.36 0.27 0.14
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![### Probability Distribution and Expected Value Calculation
**Problem Statement:**
Sally decides to do an experiment to determine how many times her MP3 player will shuffle through her songs and play her favorite group, "The Googly Girls," per hour. Her results are shown in the probability distribution table below. Find the expected value that the MP3 player will play a song by "The Googly Girls" each hour.
**Probability Distribution Table:**
| x | p(x) |
|-----|------|
| 0 | 0.23 |
| 1 | 0.36 |
| 2 | 0.27 |
| 3 | 0.14 |
**Options:**
- 0.88
- 1.15
- 1.32
- 0.71
**Calculation:**
To find the expected value (E) of the number of times a song by "The Googly Girls" is played, use the formula:
\[ E(x) = \sum [x \cdot p(x)] \]
Calculate as follows:
\[ E(x) = (0 \cdot 0.23) + (1 \cdot 0.36) + (2 \cdot 0.27) + (3 \cdot 0.14) \]
\[ E(x) = 0 + 0.36 + 0.54 + 0.42 \]
\[ E(x) = 1.32 \]
**Conclusion:**
The expected value that the MP3 player will play a song by "The Googly Girls" each hour is **1.32**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabe9e786-be4a-454e-b2cf-16d08b96c793%2Fd4bf979d-121c-4323-9d6e-8d40da4ced93%2Fwphna16_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Distribution and Expected Value Calculation
**Problem Statement:**
Sally decides to do an experiment to determine how many times her MP3 player will shuffle through her songs and play her favorite group, "The Googly Girls," per hour. Her results are shown in the probability distribution table below. Find the expected value that the MP3 player will play a song by "The Googly Girls" each hour.
**Probability Distribution Table:**
| x | p(x) |
|-----|------|
| 0 | 0.23 |
| 1 | 0.36 |
| 2 | 0.27 |
| 3 | 0.14 |
**Options:**
- 0.88
- 1.15
- 1.32
- 0.71
**Calculation:**
To find the expected value (E) of the number of times a song by "The Googly Girls" is played, use the formula:
\[ E(x) = \sum [x \cdot p(x)] \]
Calculate as follows:
\[ E(x) = (0 \cdot 0.23) + (1 \cdot 0.36) + (2 \cdot 0.27) + (3 \cdot 0.14) \]
\[ E(x) = 0 + 0.36 + 0.54 + 0.42 \]
\[ E(x) = 1.32 \]
**Conclusion:**
The expected value that the MP3 player will play a song by "The Googly Girls" each hour is **1.32**.
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