Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. the area of the shaded region is ? This image displays two pages of a Standard Normal Distribution Table, used in statistics to find the probability that a statistic is observed below, above, or between values on the standard normal curve.### Page 1:- **Z-Scores and Area Values**: The table on the left provides z-scores ranging from -3.4 to 0.0 in increments of 0.1. For each main z-score value listed in the leftmost column, corresponding probabilities are given in the row for subsequent hundredths from 0.00 to 0.09. - **Interpretation**: This table helps in determining the area (or probability) to the left of a given z-score on a standard normal distribution curve. For example, a z-score of -1.5 corresponds to a probability of 0.0668.- **Special Notes**: For z values below -1.94, use 0.0001 for the area. Also, the table provides common areas through interpolation for z = -1.645 (Area = 0.0500) and z = -2.575 (Area = 0.0050).### Page 2:- **Z-Scores and Area Values**: The table on the right continues from z = 1.3 to 3.4, again detailed in increments of 0.1 with values for hundredths ranging from 0.00 to 0.09.- **Interpretation**: This part of the table is used to find the area to the left of positive z-scores. For instance, a z-score of 2.0 gives an area of 0.9772.- **Special Notes**: For z values above 3.49, use 0.9999 for the area. The table also provides critical z-values and areas for confidence levels 90% (z = 1.645), 95% (z = 1.96), and 99% (z = 2.575).### Common Critical Values:- 90% Confidence Level: Critical value z = 1.645- 95% Confidence Level: Critical value z = 1.96- 99% Confidence Level: Critical value z = 2.575This table is essential in hypothesis testing and confidence interval construction in statistics, serving as a reference for determining the tail probabilities of a standard normal distribution. The image displays a standard normal distribution curve, commonly known as a bell curve. The curve is symmetrical, indicating a normal distribution of data. The area highlighted in teal under the curve represents the probability or proportion of data points that fall below a certain Z-score, in this case, $ z = 0.34 $.This Z-score is marked by a vertical line on the curve. A Z-score of 0.34 suggests that the data point is 0.34 standard deviations above the mean of the distribution. The shaded area to the left of this line indicates the cumulative probability associated with this Z-score.Understanding Z-scores is important in statistics as it allows comparison of data points from different normal distributions by standardizing them.

We have to find the area of the shaded region. The shaded region is z=0.34.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

the area of the shaded region is ?

This image displays two pages of a Standard Normal Distribution Table, used in statistics to find the probability that a statistic is observed below, above, or between values on the standard normal curve.

### Page 1:

- **Z-Scores and Area Values**: The table on the left provides z-scores ranging from -3.4 to 0.0 in increments of 0.1. For each main z-score value listed in the leftmost column, corresponding probabilities are given in the row for subsequent hundredths from 0.00 to 0.09.

- **Interpretation**: This table helps in determining the area (or probability) to the left of a given z-score on a standard normal distribution curve. For example, a z-score of -1.5 corresponds to a probability of 0.0668.

- **Special Notes**: For z values below -1.94, use 0.0001 for the area. Also, the table provides common areas through interpolation for z = -1.645 (Area = 0.0500) and z = -2.575 (Area = 0.0050).

### Page 2:

- **Z-Scores and Area Values**: The table on the right continues from z = 1.3 to 3.4, again detailed in increments of 0.1 with values for hundredths ranging from 0.00 to 0.09.

- **Interpretation**: This part of the table is used to find the area to the left of positive z-scores. For instance, a z-score of 2.0 gives an area of 0.9772.

- **Special Notes**: For z values above 3.49, use 0.9999 for the area. The table also provides critical z-values and areas for confidence levels 90% (z = 1.645), 95% (z = 1.96), and 99% (z = 2.575).

### Common Critical Values:
- 90% Confidence Level: Critical value z = 1.645
- 95% Confidence Level: Critical value z = 1.96
- 99% Confidence Level: Critical value z = 2.575

This table is essential in hypothesis testing and confidence interval construction in statistics, serving as a reference for determining the tail probabilities of a standard normal distribution.

The image displays a standard normal distribution curve, commonly known as a bell curve. The curve is symmetrical, indicating a normal distribution of data. The area highlighted in teal under the curve represents the probability or proportion of data points that fall below a certain Z-score, in this case, $ z = 0.34 $.

This Z-score is marked by a vertical line on the curve. A Z-score of 0.34 suggests that the data point is 0.34 standard deviations above the mean of the distribution. The shaded area to the left of this line indicates the cumulative probability associated with this Z-score.

Understanding Z-scores is important in statistics as it allows comparison of data points from different normal distributions by standardizing them.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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