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A normal distribution has a mean of 40 and a standard deviation of 4. Find the probability that a randomly selected x-value from the distribution is in the given interval + 24 + T 28 32 36 % T 40 X 44 48 52 + 56

A normal distribution has a mean of 40 and a standard deviation of 4. Find the probability that a randomly selected x-value from the distribution is in the given interval + 24 + T 28 32 36 % T 40 X 44 48 52 + 56

MATLAB: An Introduction with Applications
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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**Title: Exploring Probability in a Normal Distribution** **Introduction:** This section examines a normal distribution with a mean (\(\mu\)) of 40 and a standard deviation (\(\sigma\)) of 4. The task is to determine the probability that a randomly selected x-value from this distribution falls within specified intervals. **Graph Explanation:** 1. **First Graph:** - **Description:** The graph represents a normal distribution curve shaded in blue. - **Parameters:** - Mean (\(\mu\)) = 40 - Standard Deviation (\(\sigma\)) = 4 - **Interval Shaded (in Blue):** The interval is from 32 to 48 on the x-axis. - **Purpose:** To find the probability that a randomly selected value falls between 32 and 48. - **Input Field:** There is a blank box to input the calculated probability percentage. 2. **Second Graph:** - **Description:** A similar normal distribution curve, with a blue shaded area. - **Interval Shaded (in Blue):** The interval is from 44 to 48 on the x-axis. - **Purpose:** To find the probability that a randomly selected value falls between 44 and 48. - **Input Field:** There is a blank box to input the calculated probability percentage. **Conclusion:** After understanding the graph and the parameters of the normal distribution, calculate the probability for each interval. Use the properties of the normal distribution and standard deviation to determine the areas under the curve. Enter the results in the provided input fields as percentages.
Transcribed Image Text:**Title: Exploring Probability in a Normal Distribution** **Introduction:** This section examines a normal distribution with a mean (\(\mu\)) of 40 and a standard deviation (\(\sigma\)) of 4. The task is to determine the probability that a randomly selected x-value from this distribution falls within specified intervals. **Graph Explanation:** 1. **First Graph:** - **Description:** The graph represents a normal distribution curve shaded in blue. - **Parameters:** - Mean (\(\mu\)) = 40 - Standard Deviation (\(\sigma\)) = 4 - **Interval Shaded (in Blue):** The interval is from 32 to 48 on the x-axis. - **Purpose:** To find the probability that a randomly selected value falls between 32 and 48. - **Input Field:** There is a blank box to input the calculated probability percentage. 2. **Second Graph:** - **Description:** A similar normal distribution curve, with a blue shaded area. - **Interval Shaded (in Blue):** The interval is from 44 to 48 on the x-axis. - **Purpose:** To find the probability that a randomly selected value falls between 44 and 48. - **Input Field:** There is a blank box to input the calculated probability percentage. **Conclusion:** After understanding the graph and the parameters of the normal distribution, calculate the probability for each interval. Use the properties of the normal distribution and standard deviation to determine the areas under the curve. Enter the results in the provided input fields as percentages.
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