The amount of syrup that people put on their pancakes is normally distributed with mean 59 mL and standard deviation 9 mL. Suppose that 13 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N 59 ✓ 9 ✓ OF b. What is the distribution of a? N 59 ✓ 2.4962 ✓ c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60.1 mL and 62.9 mL. d. For the group of 13 pancake eaters, find the probability that the average amount of syrup is between 60.1 mL and 62.9 mL. e. For part d), is the assumption that the distribution is normal necessary? No Yes d Textbook Pages 5.71/10 pts 2-399 Submit Question Question 3 میں Details
The amount of syrup that people put on their pancakes is normally distributed with mean 59 mL and standard deviation 9 mL. Suppose that 13 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N 59 ✓ 9 ✓ OF b. What is the distribution of a? N 59 ✓ 2.4962 ✓ c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60.1 mL and 62.9 mL. d. For the group of 13 pancake eaters, find the probability that the average amount of syrup is between 60.1 mL and 62.9 mL. e. For part d), is the assumption that the distribution is normal necessary? No Yes d Textbook Pages 5.71/10 pts 2-399 Submit Question Question 3 میں Details
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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Help with c and d
![### Problem Statement:
The amount of syrup that people put on their pancakes is normally distributed with a mean of 59 mL and a standard deviation of 9 mL. Suppose that 13 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
#### a. What is the distribution of \( X \)?
\( X \sim N\left(59, 9\right) \)
#### b. What is the distribution of \( \bar{x} \)?
\( \bar{x} \sim N\left(59, \frac{9}{\sqrt{13}}\right) \)
To find \( \frac{9}{\sqrt{13}} \):
\[ \frac{9}{\sqrt{13}} \approx 2.4962 \]
\[ \bar{x} \sim N\left(59, 2.4962\right) \]
#### c. If a single randomly selected individual is observed, find the probability that this person consumes between 60.1 mL and 62.9 mL.
\[ P(60.1 \leq X \leq 62.9) = ? \]
#### d. For the group of 13 pancake eaters, find the probability that the average amount of syrup is between 60.1 mL and 62.9 mL.
\[ P(60.1 \leq \bar{x} \leq 62.9) = ? \]
#### e. For part (d), is the assumption that the distribution is normal necessary?
\[ \text{Yes} \]
### Hint:
- [Hint](#)
- [Textbook Pages](#)
### Additional Notes:
- This problem is an example of how the normal distribution can be applied to real-world data.
- It involves understanding and applying the properties of the normal distribution, especially the mean and standard deviation.
**Submit Question Button:**
Ensure to verify your answers and calculations before pressing the submit button for evaluation.
### Graph Explanation:
There are no graphs or diagrams in this image, the problem is entirely text-based.
**Scoring Notes:**
- This question has allocated scores of 5.71/10 points and has been attempted by 99 users.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba867a91-7946-4dc8-8b92-57b0d80fa10e%2Ffecb762a-203f-4d8f-9de7-d0f1e1dc4b1e%2Fgk8chre_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
The amount of syrup that people put on their pancakes is normally distributed with a mean of 59 mL and a standard deviation of 9 mL. Suppose that 13 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
#### a. What is the distribution of \( X \)?
\( X \sim N\left(59, 9\right) \)
#### b. What is the distribution of \( \bar{x} \)?
\( \bar{x} \sim N\left(59, \frac{9}{\sqrt{13}}\right) \)
To find \( \frac{9}{\sqrt{13}} \):
\[ \frac{9}{\sqrt{13}} \approx 2.4962 \]
\[ \bar{x} \sim N\left(59, 2.4962\right) \]
#### c. If a single randomly selected individual is observed, find the probability that this person consumes between 60.1 mL and 62.9 mL.
\[ P(60.1 \leq X \leq 62.9) = ? \]
#### d. For the group of 13 pancake eaters, find the probability that the average amount of syrup is between 60.1 mL and 62.9 mL.
\[ P(60.1 \leq \bar{x} \leq 62.9) = ? \]
#### e. For part (d), is the assumption that the distribution is normal necessary?
\[ \text{Yes} \]
### Hint:
- [Hint](#)
- [Textbook Pages](#)
### Additional Notes:
- This problem is an example of how the normal distribution can be applied to real-world data.
- It involves understanding and applying the properties of the normal distribution, especially the mean and standard deviation.
**Submit Question Button:**
Ensure to verify your answers and calculations before pressing the submit button for evaluation.
### Graph Explanation:
There are no graphs or diagrams in this image, the problem is entirely text-based.
**Scoring Notes:**
- This question has allocated scores of 5.71/10 points and has been attempted by 99 users.
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