A normal distribution has a mean of u standard deviation of o = 12. For each of the follow- ing scores, indicate whether the body is to the right or

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### Understanding Normal Distributions

**Problem 13:**

A normal distribution has a mean (\(\mu\)) of 30 and a standard deviation (\(\sigma\)) of 12. For each of the following scores, indicate whether the body is to the right or left.

---

This problem involves understanding the placement of scores within a normal distribution. Given the mean (\(\mu = 30\)) and standard deviation (\(\sigma = 12\)), you will determine the position of given scores relative to the mean.

- **Mean (\(\mu\))**: The average or central value of a data set.
- **Standard Deviation (\(\sigma\))**: A measure of the amount of variation or dispersion in a set of values.

For any score:

- If it is greater than the mean, the body is to the left.
- If it is less than the mean, the body is to the right. 

This problem can help illustrate concepts of probability and data analysis using the normal distribution model.
Transcribed Image Text:### Understanding Normal Distributions **Problem 13:** A normal distribution has a mean (\(\mu\)) of 30 and a standard deviation (\(\sigma\)) of 12. For each of the following scores, indicate whether the body is to the right or left. --- This problem involves understanding the placement of scores within a normal distribution. Given the mean (\(\mu = 30\)) and standard deviation (\(\sigma = 12\)), you will determine the position of given scores relative to the mean. - **Mean (\(\mu\))**: The average or central value of a data set. - **Standard Deviation (\(\sigma\))**: A measure of the amount of variation or dispersion in a set of values. For any score: - If it is greater than the mean, the body is to the left. - If it is less than the mean, the body is to the right. This problem can help illustrate concepts of probability and data analysis using the normal distribution model.
Transcribe the image as part of educational content:

---

**Question:**

For each of the following scores, calculate the area to the left of the score and find the proportion of the distribution located in the body.

a. \( X = 33 \)  
b. \( X = 18 \)  
c. \( X = 24 \)  
d. \( X = 39 \)  

--- 

This activity requires understanding of statistical distributions, often using the context of normal distributions. Students should use statistical tables or software to find the corresponding areas for each of the scores listed.
Transcribed Image Text:Transcribe the image as part of educational content: --- **Question:** For each of the following scores, calculate the area to the left of the score and find the proportion of the distribution located in the body. a. \( X = 33 \) b. \( X = 18 \) c. \( X = 24 \) d. \( X = 39 \) --- This activity requires understanding of statistical distributions, often using the context of normal distributions. Students should use statistical tables or software to find the corresponding areas for each of the scores listed.
Expert Solution
a. X = 33:

Given info:

Here, mean, µ = 30 and σ = 12

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