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69 78 87 96 105 114 Based on the graph of this normal distribution, a. The mean is b. The median is c. The mode is d. The standard deviation is 123

69 78 87 96 105 114 Based on the graph of this normal distribution, a. The mean is b. The median is c. The mode is d. The standard deviation is 123

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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### Understanding the Normal Distribution In this section, we explore the properties of a standard normal distribution through the given graph. #### **Graph Description:** The graph represents a normal distribution curve. It is centered at the mean value, with a symmetric bell-shaped curve. Here, the horizontal axis (x-axis) indicates the values of the variable, ranging from 69 to 123. Key values on the x-axis are marked and spaced at intervals: - 69 - 78 - 87 - 96 - 105 - 114 - 123 #### **Questions:** Based on the graph of this normal distribution, fill in the blanks for the following questions: a. The mean is ___ . b. The median is ___ . c. The mode is ___ . d. The standard deviation is ___ . #### **Explanation:** To accurately answer these questions, observe the following properties of the normal distribution: - **Mean (μ):** The peak (or center) of the normal distribution curve. - **Median:** The value that divides the distribution into two equal halves. For a normal distribution, this is equal to the mean. - **Mode:** The value that appears most frequently in the data set. For a perfectly normal distribution, this also equates to the mean. - **Standard Deviation (σ):** A measure of the spread or dispersion of the distribution. Since the graph is of a standard normal distribution, the values of mean, median, and mode will be the same and located at the center of the curve. The standard deviation can be derived from the given range. Please examine the graph closely to find these values and complete the blanks accurately.
Transcribed Image Text:### Understanding the Normal Distribution In this section, we explore the properties of a standard normal distribution through the given graph. #### **Graph Description:** The graph represents a normal distribution curve. It is centered at the mean value, with a symmetric bell-shaped curve. Here, the horizontal axis (x-axis) indicates the values of the variable, ranging from 69 to 123. Key values on the x-axis are marked and spaced at intervals: - 69 - 78 - 87 - 96 - 105 - 114 - 123 #### **Questions:** Based on the graph of this normal distribution, fill in the blanks for the following questions: a. The mean is ___ . b. The median is ___ . c. The mode is ___ . d. The standard deviation is ___ . #### **Explanation:** To accurately answer these questions, observe the following properties of the normal distribution: - **Mean (μ):** The peak (or center) of the normal distribution curve. - **Median:** The value that divides the distribution into two equal halves. For a normal distribution, this is equal to the mean. - **Mode:** The value that appears most frequently in the data set. For a perfectly normal distribution, this also equates to the mean. - **Standard Deviation (σ):** A measure of the spread or dispersion of the distribution. Since the graph is of a standard normal distribution, the values of mean, median, and mode will be the same and located at the center of the curve. The standard deviation can be derived from the given range. Please examine the graph closely to find these values and complete the blanks accurately.
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