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A normal distribution has a mean of 40 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval 16 - 22 28 34 % 40 X 46 52 58 64

A normal distribution has a mean of 40 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval 16 - 22 28 34 % 40 X 46 52 58 64

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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## Normal Distribution Probability A normal distribution has a mean of 40 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval. ### Graph 1 The graph displays a bell-shaped normal distribution curve. The mean of 40 is marked at the center of the curve, and the distribution is symmetric around this mean. The x-axis is labeled with values from 16 to 64, indicating the range of x-values. A section of the curve is shaded in blue, covering the central area around the mean. The specific x-values marking the boundaries of the shaded area are not provided, but this typically represents a common probability interval such as 68%, 95%, or 99.7% based on standard deviation rules. **Input Box:** A text field is provided below the graph for inputting the probability percentage of the shaded area. ### Graph 2 This graph also depicts a normal distribution curve, similar to the first, with a mean of 40. The x-axis ranges from 16 to 64. In this graph, a smaller section on the right side of the mean is shaded in blue, specifically between x-values 46 and 52. This portion of the curve represents the probability of the x-value falling within this narrower interval. **Input Box:** Another text field is provided below the second graph for inputting the probability percentage of the shaded area. These graphs help visualize the concept of probability within the context of a normal distribution by highlighting different intervals and allowing users to compute the likelihood of occurrence within those intervals.
Transcribed Image Text:## Normal Distribution Probability A normal distribution has a mean of 40 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval. ### Graph 1 The graph displays a bell-shaped normal distribution curve. The mean of 40 is marked at the center of the curve, and the distribution is symmetric around this mean. The x-axis is labeled with values from 16 to 64, indicating the range of x-values. A section of the curve is shaded in blue, covering the central area around the mean. The specific x-values marking the boundaries of the shaded area are not provided, but this typically represents a common probability interval such as 68%, 95%, or 99.7% based on standard deviation rules. **Input Box:** A text field is provided below the graph for inputting the probability percentage of the shaded area. ### Graph 2 This graph also depicts a normal distribution curve, similar to the first, with a mean of 40. The x-axis ranges from 16 to 64. In this graph, a smaller section on the right side of the mean is shaded in blue, specifically between x-values 46 and 52. This portion of the curve represents the probability of the x-value falling within this narrower interval. **Input Box:** Another text field is provided below the second graph for inputting the probability percentage of the shaded area. These graphs help visualize the concept of probability within the context of a normal distribution by highlighting different intervals and allowing users to compute the likelihood of occurrence within those intervals.
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