Determine whether the following graph can represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation. A 10 15 20 25 30 OA. Yes, the graph fulfills the properties of the normal distribution. The mean is approximately and the standard deviation is about (Type whole numbers.) OB. No, because the graph crosses the x-axis. OC. No, because the graph is skewed left. O D. No, because the graph is skewed right. 4 Could the graph represent a variable with a normal distribution? Explain your reasoning. Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
Determine whether the following graph can represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation. A 10 15 20 25 30 OA. Yes, the graph fulfills the properties of the normal distribution. The mean is approximately and the standard deviation is about (Type whole numbers.) OB. No, because the graph crosses the x-axis. OC. No, because the graph is skewed left. O D. No, because the graph is skewed right. 4 Could the graph represent a variable with a normal distribution? Explain your reasoning. Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
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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![### Analyzing Normal Distribution
**Task:**
Determine whether the following graph can represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.
**Graph Description:**
The provided graph is a bell-shaped curve, indicative of a normal distribution. The x-axis is labeled, showing a range from 10 to 30, with tick marks at intervals of 5 (i.e., 10, 15, 20, 25, 30).
**Question:**
Could the graph represent a variable with a normal distribution? Explain your reasoning. Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
**Answer Choices:**
- **A.** Yes, the graph fulfills the properties of the normal distribution. The mean is approximately [____] and the standard deviation is about [____]. (Type whole numbers.)
- **B.** No, because the graph crosses the x-axis.
- **C.** No, because the graph is skewed left.
- **D.** No, because the graph is skewed right.
---
**Explanation of Normal Distribution:**
A normal distribution, also known as the Gaussian distribution, is characterized by a symmetric bell-shaped curve. The majority of the data points lie close to the mean, and the curve tapers off equally on both sides away from the mean.
To determine if the provided graph represents a normal distribution:
1. **Symmetry:** Check if the curve is symmetrical around the center.
2. **Peak:** Identify whether the graph peaks at a central point.
3. **Tapering:** Observe if both tails (left and right sides of the peak) have equal tapering.
Since the graph appears symmetrical and peaks at around the same central value, it suggests that it may represent a normal distribution.
**Estimating Mean and Standard Deviation:**
- **Mean (μ):** The mean is the central value where the peak occurs. Based on the graph, the peak appears roughly around the value of 20.
- **Standard Deviation (σ):** The standard deviation can be estimated based on the spread of the graph. The graph ranges from approximately 10 to 30, so an estimate might place the standard deviation around 5.
**Optimal Choice:**
- **A.** Yes, the graph fulfills the properties of the normal distribution. The mean is approximately 20 and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febc6c9e4-20c2-4aa0-9f79-b773de998cf1%2F42a08f71-13b1-414f-8c73-81d545482018%2Fwnbv30h_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing Normal Distribution
**Task:**
Determine whether the following graph can represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.
**Graph Description:**
The provided graph is a bell-shaped curve, indicative of a normal distribution. The x-axis is labeled, showing a range from 10 to 30, with tick marks at intervals of 5 (i.e., 10, 15, 20, 25, 30).
**Question:**
Could the graph represent a variable with a normal distribution? Explain your reasoning. Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
**Answer Choices:**
- **A.** Yes, the graph fulfills the properties of the normal distribution. The mean is approximately [____] and the standard deviation is about [____]. (Type whole numbers.)
- **B.** No, because the graph crosses the x-axis.
- **C.** No, because the graph is skewed left.
- **D.** No, because the graph is skewed right.
---
**Explanation of Normal Distribution:**
A normal distribution, also known as the Gaussian distribution, is characterized by a symmetric bell-shaped curve. The majority of the data points lie close to the mean, and the curve tapers off equally on both sides away from the mean.
To determine if the provided graph represents a normal distribution:
1. **Symmetry:** Check if the curve is symmetrical around the center.
2. **Peak:** Identify whether the graph peaks at a central point.
3. **Tapering:** Observe if both tails (left and right sides of the peak) have equal tapering.
Since the graph appears symmetrical and peaks at around the same central value, it suggests that it may represent a normal distribution.
**Estimating Mean and Standard Deviation:**
- **Mean (μ):** The mean is the central value where the peak occurs. Based on the graph, the peak appears roughly around the value of 20.
- **Standard Deviation (σ):** The standard deviation can be estimated based on the spread of the graph. The graph ranges from approximately 10 to 30, so an estimate might place the standard deviation around 5.
**Optimal Choice:**
- **A.** Yes, the graph fulfills the properties of the normal distribution. The mean is approximately 20 and
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