
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Card Game Probability Analysis**
You are playing a card game, and the probability that you will win a game is \( p = 0.45 \).
**Question 1: Expected Wins**
If you play the game 764 times, what is the most likely number of wins?
*(Round the answer to one decimal place.)*
\[ \mu = \_\_\_\_ \]
**Question 2: Standard Deviation**
Let \( X \) represent the number of games (out of 764) that you win. Find the standard deviation for the probability distribution of \( X \).
*(Round the answer to two decimal places.)*
\[ \sigma = \_\_\_\_ \]
**Range Rule of Thumb**
The range rule of thumb specifies that the minimum usual value for a random variable is \( \mu - 2\sigma \) and the maximum usual value is \( \mu + 2\sigma \). You already found \( \mu \) and \( \sigma \) for the random variable \( X \).
**Question 3: Usual Range**
Use the range rule of thumb to find the usual range of \( X \) values. Enter the answer as an interval using square brackets and only whole numbers.
\[ \text{usual values} = \_\_\_\_ \]](https://content.bartleby.com/qna-images/question/f085ba7b-ac04-4072-bb4a-16fcbd016e3e/5fc3f61e-a079-4e8b-9de8-895417d8f3e5/9vbxw1b_thumbnail.jpeg)
Transcribed Image Text:**Card Game Probability Analysis**
You are playing a card game, and the probability that you will win a game is \( p = 0.45 \).
**Question 1: Expected Wins**
If you play the game 764 times, what is the most likely number of wins?
*(Round the answer to one decimal place.)*
\[ \mu = \_\_\_\_ \]
**Question 2: Standard Deviation**
Let \( X \) represent the number of games (out of 764) that you win. Find the standard deviation for the probability distribution of \( X \).
*(Round the answer to two decimal places.)*
\[ \sigma = \_\_\_\_ \]
**Range Rule of Thumb**
The range rule of thumb specifies that the minimum usual value for a random variable is \( \mu - 2\sigma \) and the maximum usual value is \( \mu + 2\sigma \). You already found \( \mu \) and \( \sigma \) for the random variable \( X \).
**Question 3: Usual Range**
Use the range rule of thumb to find the usual range of \( X \) values. Enter the answer as an interval using square brackets and only whole numbers.
\[ \text{usual values} = \_\_\_\_ \]
![Assume that a procedure yields a binomial distribution with \( n = 963 \) trials and the probability of success for one trial is \( p = 17\% \).
1. **Find the mean for this binomial distribution.**
- *(Round answer to one decimal place.)*
- \( \mu = \underline{\hspace{3cm}} \)
2. **Find the standard deviation for this distribution.**
- *(Round answer to two decimal places.)*
- \( \sigma = \underline{\hspace{3cm}} \)
3. **Use the range rule of thumb to find the minimum usual value \(\mu - 2\sigma\) and the maximum usual value \(\mu + 2\sigma\). Enter answer as an interval using square-brackets only with whole numbers.**
- usual values = \([\underline{\hspace{2cm}}, \underline{\hspace{2cm}}]\)](https://content.bartleby.com/qna-images/question/f085ba7b-ac04-4072-bb4a-16fcbd016e3e/5fc3f61e-a079-4e8b-9de8-895417d8f3e5/z7yh9r_thumbnail.jpeg)
Transcribed Image Text:Assume that a procedure yields a binomial distribution with \( n = 963 \) trials and the probability of success for one trial is \( p = 17\% \).
1. **Find the mean for this binomial distribution.**
- *(Round answer to one decimal place.)*
- \( \mu = \underline{\hspace{3cm}} \)
2. **Find the standard deviation for this distribution.**
- *(Round answer to two decimal places.)*
- \( \sigma = \underline{\hspace{3cm}} \)
3. **Use the range rule of thumb to find the minimum usual value \(\mu - 2\sigma\) and the maximum usual value \(\mu + 2\sigma\). Enter answer as an interval using square-brackets only with whole numbers.**
- usual values = \([\underline{\hspace{2cm}}, \underline{\hspace{2cm}}]\)
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