Let z be a standard normal random variable with mean ? = 0 and standard deviation ? = 1. Use Table 3 in Appendix I to find the probability. (Round your answer to four decimal places.)P(z > 1.12) = ### Z-Score Table (Continued)This table represents a continuation of the z-score table used in statistics to find the probability of a standard normal distribution. Each cell contains the cumulative probability for a standard normal random variable, corresponding to z-scores.#### Table Layout- **Rows and Columns**: The table is divided into sections with z-scores represented in rows and columns. - The z-scores proceed vertically from 0.0 to 3.4 in increments of 0.1 in the first column. - The top row contains the second decimal place of the z-score, ranging from .00 to .09.#### How to Read the Table - For a given z-score, find the row for the first two digits and the column for the second decimal digit. The value at this intersection is the cumulative probability that a standard normal variable is less than or equal to that z-score.#### Example- To find the probability for a z-score of 2.56: - Locate the row starting with 2.5. - Move to the column under .06. - The value in this cell is 0.9948. This value signifies that there is a 99.48% chance that a data point is below a z-score of 2.56 in a standard normal distribution.This table is an essential tool in statistics for determining percentiles, calculating probabilities, and conducting hypothesis testing using the standard normal distribution. # Table 3: Areas under the Normal CurveThis table provides the cumulative areas under the standard normal distribution curve for a range of z-values. It is used to find the probability that a standard normal random variable is less than or equal to a given z-value.### Explanation of How to Use the Table- **z**: Represents the z-score, which indicates how many standard deviations away from the mean a data point is.- **Columns (.00 to .09)**: Each column represents the hundredth decimal place of the z-score.### Structure:- The first column lists the whole and tenths part of the z-scores, ranging from -3.4 to 0.0.- Each subsequent column represents the additional hundredths digit appended to the z-score.### Example:- To find the area under the curve for a z-score of -1.26: - Locate -1.2 in the first column. - Move across to the column under .06. - The intersection gives the area: .1038.### Table Data:The entries are cumulative probabilities. For any given z-score, the value in the table represents the area under the curve to the left of that z-score.- For z = -3.4, area = .0003- For z = -2.0, area = .0228- For z = -1.0, area = .1587- For z = 0.0, area = .5000### Applications:This table is widely used in statistics for hypothesis testing, finding probabilities related to normal distributions, and standardizing different datasets. Understanding the areas under the normal curve is essential for calculating z-scores, confidence intervals, and conducting various statistical analyses.

Given that Z is standard normal random variable. Mean (μ) = 0 Standard deviation (σ) = 1

Answered: P(z > 1.12)

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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Let z be a standard normal random variable with mean ? = 0 and standard deviation ? = 1. Use Table 3 in Appendix I to find the probability. (Round your answer to four decimal places.)

P(z > 1.12) =

### Z-Score Table (Continued)

This table represents a continuation of the z-score table used in statistics to find the probability of a standard normal distribution. Each cell contains the cumulative probability for a standard normal random variable, corresponding to z-scores.

#### Table Layout

- **Rows and Columns**: The table is divided into sections with z-scores represented in rows and columns.
- The z-scores proceed vertically from 0.0 to 3.4 in increments of 0.1 in the first column.
- The top row contains the second decimal place of the z-score, ranging from .00 to .09.

#### How to Read the Table

- For a given z-score, find the row for the first two digits and the column for the second decimal digit. The value at this intersection is the cumulative probability that a standard normal variable is less than or equal to that z-score.

#### Example

- To find the probability for a z-score of 2.56:
- Locate the row starting with 2.5.
- Move to the column under .06.
- The value in this cell is 0.9948.

This value signifies that there is a 99.48% chance that a data point is below a z-score of 2.56 in a standard normal distribution.

This table is an essential tool in statistics for determining percentiles, calculating probabilities, and conducting hypothesis testing using the standard normal distribution.

# Table 3: Areas under the Normal Curve

This table provides the cumulative areas under the standard normal distribution curve for a range of z-values. It is used to find the probability that a standard normal random variable is less than or equal to a given z-value.

### Explanation of How to Use the Table

- **z**: Represents the z-score, which indicates how many standard deviations away from the mean a data point is.

- **Columns (.00 to .09)**: Each column represents the hundredth decimal place of the z-score.

### Structure:

- The first column lists the whole and tenths part of the z-scores, ranging from -3.4 to 0.0.
- Each subsequent column represents the additional hundredths digit appended to the z-score.

### Example:

- To find the area under the curve for a z-score of -1.26:
- Locate -1.2 in the first column.
- Move across to the column under .06.
- The intersection gives the area: .1038.

### Table Data:

The entries are cumulative probabilities. For any given z-score, the value in the table represents the area under the curve to the left of that z-score.

- For z = -3.4, area = .0003
- For z = -2.0, area = .0228
- For z = -1.0, area = .1587
- For z = 0.0, area = .5000

### Applications:

This table is widely used in statistics for hypothesis testing, finding probabilities related to normal distributions, and standardizing different datasets. Understanding the areas under the normal curve is essential for calculating z-scores, confidence intervals, and conducting various statistical analyses.

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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