4) Which score has a better position? (show your calculations of the z-scores) A score of 33.1 on a test with a sample mean of 28 and s= 5 or A score of 289.7 on a test with a sample mean of 268 and s =19?
4) Which score has a better position? (show your calculations of the z-scores) A score of 33.1 on a test with a sample mean of 28 and s= 5 or A score of 289.7 on a test with a sample mean of 268 and s =19?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Can you help with # 4 on my hw pls
![### Probability and Statistics Exercise
#### Comparing Z-Scores
**Question 4:**
Which score has a better position? (show your calculations of the z-scores)
- A score of 33.1 on a test with a sample mean of 28 and \( s = 5 \) or
- A score of 289.7 on a test with a sample mean of 268 and \( s = 19 \)
**Solution:**
To determine which score has a better position, we need to calculate the z-scores for both test scores.
The z-score formula is:
\[ z = \frac{(X - \mu)}{s} \]
Where:
- \( X \) is the score
- \( \mu \) is the sample mean
- \( s \) is the standard deviation
For the first test score:
\[ X = 33.1, \mu = 28, s = 5 \]
\[ z = \frac{(33.1 - 28)}{5} = \frac{5.1}{5} = 1.02 \]
For the second test score:
\[ X = 289.7, \mu = 268, s = 19 \]
\[ z = \frac{(289.7 - 268)}{19} = \frac{21.7}{19} \approx 1.14 \]
Conclusion: The second score has a better position because it has a higher z-score.
#### Probability Question
**Question 5:**
Use the following table to answer the probability questions:
| Waiting time (minutes) | Number of customers |
|------------------------|---------------------|
| 0-3 | 14 |
| 4-7 | 9 |
| 8-11 | 11 |
This table shows the number of customers corresponding to different waiting times.
**Instructions:**
Use this table to calculate probabilities related to customer waiting times. For example, to find the probability that a customer's waiting time is between 4 and 7 minutes, divide the number of customers in that range by the total number of customers.
**Calculations:**
Total number of customers = \( 14 + 9 + 11 = 34 \)
Probability that a customer's waiting time is 0-3 minutes:
\[ P(0-3) = \frac{14}{34} \approx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6ad1cd7-e883-4155-acb4-5513247aaa08%2Fb9af5b24-4006-4a66-976c-3fba98e8fca8%2Fw8qgta_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics Exercise
#### Comparing Z-Scores
**Question 4:**
Which score has a better position? (show your calculations of the z-scores)
- A score of 33.1 on a test with a sample mean of 28 and \( s = 5 \) or
- A score of 289.7 on a test with a sample mean of 268 and \( s = 19 \)
**Solution:**
To determine which score has a better position, we need to calculate the z-scores for both test scores.
The z-score formula is:
\[ z = \frac{(X - \mu)}{s} \]
Where:
- \( X \) is the score
- \( \mu \) is the sample mean
- \( s \) is the standard deviation
For the first test score:
\[ X = 33.1, \mu = 28, s = 5 \]
\[ z = \frac{(33.1 - 28)}{5} = \frac{5.1}{5} = 1.02 \]
For the second test score:
\[ X = 289.7, \mu = 268, s = 19 \]
\[ z = \frac{(289.7 - 268)}{19} = \frac{21.7}{19} \approx 1.14 \]
Conclusion: The second score has a better position because it has a higher z-score.
#### Probability Question
**Question 5:**
Use the following table to answer the probability questions:
| Waiting time (minutes) | Number of customers |
|------------------------|---------------------|
| 0-3 | 14 |
| 4-7 | 9 |
| 8-11 | 11 |
This table shows the number of customers corresponding to different waiting times.
**Instructions:**
Use this table to calculate probabilities related to customer waiting times. For example, to find the probability that a customer's waiting time is between 4 and 7 minutes, divide the number of customers in that range by the total number of customers.
**Calculations:**
Total number of customers = \( 14 + 9 + 11 = 34 \)
Probability that a customer's waiting time is 0-3 minutes:
\[ P(0-3) = \frac{14}{34} \approx
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