### Analysis of the Sampling Distribution of the Sample Means**Task:** The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning.#### Provided Information and Graphs:* **Population Distribution Statistics:** - Mean ($\mu$) = 16.8 seconds - Standard Deviation ($\sigma$) = 11.2 seconds* **Graphs:** 1. **Graph (a):** - Depicts a normal distribution centered at 16.8 with the standard deviations $ \sigma_{\bar{x}} = 1.12 $. 2. **Graph (b):** - Depicts a normal distribution centered at 16.8 with the standard deviations $ \sigma_{\bar{x}} = 11.2 $. 3. **Graph (c):** - Depicts a normal distribution centered at 16.8 with the standard deviations $ \sigma_{\bar{x}} = 1.12 $.#### Explanation and Solution:To solve this task, we need to determine which graph most closely matches the sample distribution of the sample means for a sample size ($n$) of 100.1. **Calculation of the Standard Error of the Mean ($\sigma_{\bar{x}}$)**: - The formula to calculate the standard error is: \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] - Given $\sigma = 11.2$ and $n = 100$: \[ \sigma_{\bar{x}} = \frac{11.2}{\sqrt{100}} = \frac{11.2}{10} = 1.12 \]2. **Determining the Most Accurate Graph**: - The mean of the sampling distribution should remain the same: $\mu_{\bar{x}} = \mu = 16.8$. - The standard deviation of the sampling distribution should be the calculated standard error: $\sigma_{\bar{x}} = 1.12$.Upon examining the graphs:- **Graph (a)** depicts \

Name: ### Analysis of the Sampling Distribution of the Sample Means**Task:*
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Description: ### Analysis of the Sampling Distribution of the Sample Means**Task:** The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the popu

Given data: Sample size (n) = 100 Mean = 16.8

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The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning. P(x) 0.04- 0.024P (x) o: =11.2 P(x) = 11.2 AP (x) 0.454 o = 1.12 = 16.8 O = 11.2 iH=6.8 H16.8 IH= 16.8 0- 0- -20 50 Time (in sec.) 50 50 Time (in sec.) 50 Time (in sec.) Time (in sec.) Graph V most closely resembles the sampling distribution of the sample means, because u- = |,0; =, and the graph (Type an integer or a decimal.)

The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning. P(x) 0.04- 0.024P (x) o: =11.2 P(x) = 11.2 AP (x) 0.454 o = 1.12 = 16.8 O = 11.2 iH=6.8 H16.8 IH= 16.8 0- 0- -20 50 Time (in sec.) 50 50 Time (in sec.) 50 Time (in sec.) Time (in sec.) Graph V most closely resembles the sampling distribution of the sample means, because u- = |,0; =, and the graph (Type an integer or a decimal.)

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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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

### Analysis of the Sampling Distribution of the Sample Means

**Task:** The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning.

#### Provided Information and Graphs:
* **Population Distribution Statistics:**
- Mean ($\mu$) = 16.8 seconds
- Standard Deviation ($\sigma$) = 11.2 seconds

* **Graphs:**
1. **Graph (a):**
- Depicts a normal distribution centered at 16.8 with the standard deviations $ \sigma_{\bar{x}} = 1.12 $.

2. **Graph (b):**
- Depicts a normal distribution centered at 16.8 with the standard deviations $ \sigma_{\bar{x}} = 11.2 $.

3. **Graph (c):**
- Depicts a normal distribution centered at 16.8 with the standard deviations $ \sigma_{\bar{x}} = 1.12 $.

#### Explanation and Solution:
To solve this task, we need to determine which graph most closely matches the sample distribution of the sample means for a sample size ($n$) of 100.

1. **Calculation of the Standard Error of the Mean ($\sigma_{\bar{x}}$)**:
- The formula to calculate the standard error is:
\[
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
\]
- Given $\sigma = 11.2$ and $n = 100$:
\[
\sigma_{\bar{x}} = \frac{11.2}{\sqrt{100}} = \frac{11.2}{10} = 1.12
\]

2. **Determining the Most Accurate Graph**:
- The mean of the sampling distribution should remain the same: $\mu_{\bar{x}} = \mu = 16.8$.
- The standard deviation of the sampling distribution should be the calculated standard error: $\sigma_{\bar{x}} = 1.12$.

Upon examining the graphs:
- **Graph (a)** depicts \

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