he 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 225 is dra rom he population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasonim P(x) (.04- 0.04- G: =11.7 - 11.7 0.78 O=11.7 =18.9 T 18.9 18.9 04 0. 50 Time (in sec.) 50 Time (in sec.) Time (in sec.) Time (in sec.) Graph V most closely resembles the sampling distribution of the sample means, because p- =.0: = and the graph (Type an integer or a decimal.) Rel. frequency kouanbay pa

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The text presents a problem about determining which graph most closely resembles the sampling distribution of sample means for the waiting time (in seconds) at a red light.

### Description:

1. **Graphs Provided:**
   - Three graphs labeled (a), (b), and (c) are shown. Each graphs the waiting time against relative frequency.
 
2. **Graph Details:**
   - **Graph (a):**
     - Displays two curves: a solid line and a dashed line.
     - Solid line: \( \mu = 11.7 \)
     - Dashed line: \( \mu = 9.9 \)
   
   - **Graph (b):**
     - Displays two curves: a solid line and a dashed line.
     - Solid line: \( \mu = 11.7 \)
     - Dashed line: \( \mu = 18.9 \)
   
   - **Graph (c):**
     - Displays a solid line indicating sample characteristics.
     - \( \sigma_x = 0.78 \)
     - \( \mu_x = 18.9 \)

3. **Question Prompt:**
   - Determine which graph most closely resembles the sampling distribution of the sample means.
   - Input fields are provided for the mean \( \mu_{\bar{x}} \), standard deviation \( \sigma_{\bar{x}} \), and the selection of the graph.

### Interpretation:

To answer the question, consider the properties of a sampling distribution—specifically the sample mean and standard deviation. The key here is to identify how the characteristics of the sample alter the underlying graph representation.

**Input:**
- Type the identifying number for the graph.
- Enter the mean \( \mu_{\bar{x}} \) and standard deviation \( \sigma_{\bar{x}} \) of the sampling distribution.

Choose the correct graph based on the central tendency and spread that match those of the distribution derived from a sample size of 225.
Transcribed Image Text:The text presents a problem about determining which graph most closely resembles the sampling distribution of sample means for the waiting time (in seconds) at a red light. ### Description: 1. **Graphs Provided:** - Three graphs labeled (a), (b), and (c) are shown. Each graphs the waiting time against relative frequency. 2. **Graph Details:** - **Graph (a):** - Displays two curves: a solid line and a dashed line. - Solid line: \( \mu = 11.7 \) - Dashed line: \( \mu = 9.9 \) - **Graph (b):** - Displays two curves: a solid line and a dashed line. - Solid line: \( \mu = 11.7 \) - Dashed line: \( \mu = 18.9 \) - **Graph (c):** - Displays a solid line indicating sample characteristics. - \( \sigma_x = 0.78 \) - \( \mu_x = 18.9 \) 3. **Question Prompt:** - Determine which graph most closely resembles the sampling distribution of the sample means. - Input fields are provided for the mean \( \mu_{\bar{x}} \), standard deviation \( \sigma_{\bar{x}} \), and the selection of the graph. ### Interpretation: To answer the question, consider the properties of a sampling distribution—specifically the sample mean and standard deviation. The key here is to identify how the characteristics of the sample alter the underlying graph representation. **Input:** - Type the identifying number for the graph. - Enter the mean \( \mu_{\bar{x}} \) and standard deviation \( \sigma_{\bar{x}} \) of the sampling distribution. Choose the correct graph based on the central tendency and spread that match those of the distribution derived from a sample size of 225.
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