The percent of fat calories that a person consumes each day is normally distributed with a mean of about 37 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. Let X = average percent of fat calories. (a) Give the distribution of X. (Round your standard deviation to two decimal places.) (b) For the group of 16, find the probability that the average percent of fat calories consumed is more than four. (Round your answer to four decimal places.) Graph the situation and shade in the area to be determined. none 0.15 0.10 0.05 10 20 30 40 10 20 30 40 none none 0.15 0.15 0.10 0.10 0.05 0.05 20 30 40 20 30 40 (c) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.) percent of fat calories
The percent of fat calories that a person consumes each day is normally distributed with a mean of about 37 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. Let X = average percent of fat calories. (a) Give the distribution of X. (Round your standard deviation to two decimal places.) (b) For the group of 16, find the probability that the average percent of fat calories consumed is more than four. (Round your answer to four decimal places.) Graph the situation and shade in the area to be determined. none 0.15 0.10 0.05 10 20 30 40 10 20 30 40 none none 0.15 0.15 0.10 0.10 0.05 0.05 20 30 40 20 30 40 (c) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.) percent of fat calories
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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![**Transcription and Explanation for Educational Use**
---
### Content
The percent of fat calories that a person consumes each day is normally distributed with a mean of about 37 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. Let \( \bar{X} \) represent the average percent of fat calories.
**(a)** Give the distribution of \( \bar{X} \). (Round your standard deviation to two decimal places.)
\[ \bar{X} \sim N(\text{mean}, \text{standard deviation}) \]
**(b)** For the group of 16, find the probability that the average percent of fat calories consumed is more than 4. (Round your answer to four decimal places.)
Graph the situation and shade in the area to be determined.
- **Upper Left Graph:**
- X-axis: Range approximately 10 to 40
- Y-axis: Density with a peak around 0.15
- Graph is unshaded
- **Upper Right Graph:**
- X-axis: Range approximately 10 to 40
- Y-axis: Density with a peak around 0.15
- Graph is shaded on the right side
- **Lower Left Graph:**
- X-axis: Range approximately 20 to 40
- Y-axis: Density with a peak around 0.15
- Graph is shaded on the left side
- **Lower Right Graph:**
- X-axis: Range approximately 20 to 40
- Y-axis: Density with a peak around 0.15
- Graph is shaded on the right side
**(c)** Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.)
\[ \text{First quartile:} \] ___ percent of fat calories
---
**Graph Explanation**
The graphs illustrate the normal distribution of the daily percentage of fat calories consumed. Each graph displays a bell-shaped curve, highlighting various areas under the curve—some shaded, indicating different probability regions of interest. The X-axis represents the average percent of fat calories, while the Y-axis indicates the density of the distribution.
- **Shaded and Unshaded Graphs:**
- The shaded areas indicate the probability regions for specific calculation requests, such as the area representing more than a certain percentage of fat calories.
The task typically asks students to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F692b4a3d-b328-4d6d-8f5c-2ba3aed54605%2F74df1c7b-8e9b-4cf9-bf73-893f9bce8de1%2Fxknpi1p_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation for Educational Use**
---
### Content
The percent of fat calories that a person consumes each day is normally distributed with a mean of about 37 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. Let \( \bar{X} \) represent the average percent of fat calories.
**(a)** Give the distribution of \( \bar{X} \). (Round your standard deviation to two decimal places.)
\[ \bar{X} \sim N(\text{mean}, \text{standard deviation}) \]
**(b)** For the group of 16, find the probability that the average percent of fat calories consumed is more than 4. (Round your answer to four decimal places.)
Graph the situation and shade in the area to be determined.
- **Upper Left Graph:**
- X-axis: Range approximately 10 to 40
- Y-axis: Density with a peak around 0.15
- Graph is unshaded
- **Upper Right Graph:**
- X-axis: Range approximately 10 to 40
- Y-axis: Density with a peak around 0.15
- Graph is shaded on the right side
- **Lower Left Graph:**
- X-axis: Range approximately 20 to 40
- Y-axis: Density with a peak around 0.15
- Graph is shaded on the left side
- **Lower Right Graph:**
- X-axis: Range approximately 20 to 40
- Y-axis: Density with a peak around 0.15
- Graph is shaded on the right side
**(c)** Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.)
\[ \text{First quartile:} \] ___ percent of fat calories
---
**Graph Explanation**
The graphs illustrate the normal distribution of the daily percentage of fat calories consumed. Each graph displays a bell-shaped curve, highlighting various areas under the curve—some shaded, indicating different probability regions of interest. The X-axis represents the average percent of fat calories, while the Y-axis indicates the density of the distribution.
- **Shaded and Unshaded Graphs:**
- The shaded areas indicate the probability regions for specific calculation requests, such as the area representing more than a certain percentage of fat calories.
The task typically asks students to
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