Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.a. The area of the shaded region is(Round to four decimal places as needed.) The image shows a normal distribution curve, also known as a bell curve. This graph represents a probability distribution that is symmetric about its mean, indicating that data near the mean are more frequent in occurrence than data far from the mean.### Key Elements of the Graph:- **Normal Distribution Curve**: This is illustrated as a smooth, symmetric bell curve that depicts the distribution of a dataset.- **Shaded Area**: The area under the curve is shaded in light blue to signify a specific range of the data. This shaded portion typically represents the probability or percentage of data points that fall below a certain threshold.- **Vertical Line at 82**: The vertical line at the value 82 on the x-axis marks a cutoff point. This line separates the shaded area from the rest of the distribution, indicating that the shaded region includes all data points up to the value of 82.The shaded area helps visualize the proportion of the dataset that lies within a specific range, emphasizing the probability of a data point being less than or equal to 82 in this context. This type of graph is commonly used in statistics to represent data in fields such as education, research, and social sciences.

The values provided in the question are as follows, Mean (µ) = 100 Standard deviation (σ) = 15 From…

Answered: Find the area of the shaded region. The…

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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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

a. The area of the shaded region is

(Round to four decimal places as needed.)

The image shows a normal distribution curve, also known as a bell curve. This graph represents a probability distribution that is symmetric about its mean, indicating that data near the mean are more frequent in occurrence than data far from the mean.

### Key Elements of the Graph:

- **Normal Distribution Curve**: This is illustrated as a smooth, symmetric bell curve that depicts the distribution of a dataset.
- **Shaded Area**: The area under the curve is shaded in light blue to signify a specific range of the data. This shaded portion typically represents the probability or percentage of data points that fall below a certain threshold.
- **Vertical Line at 82**: The vertical line at the value 82 on the x-axis marks a cutoff point. This line separates the shaded area from the rest of the distribution, indicating that the shaded region includes all data points up to the value of 82.

The shaded area helps visualize the proportion of the dataset that lies within a specific range, emphasizing the probability of a data point being less than or equal to 82 in this context. This type of graph is commonly used in statistics to represent data in fields such as education, research, and social sciences.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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