Find the indicated probability using the standard normal distribution.P(0 < z < 0.535)P ( 0 < z < 0.535) = The image displays a portion of a standard normal distribution table, commonly used in statistics to find the probability associated with a given Z-score. This table typically shows the cumulative probability of a standard normal distribution (mean = 0, standard deviation = 1).### Transcription of the Table:The Z-score values range from -3.4 to -1.4 along the leftmost column, and the probabilities for each hundredth place are provided across the top row, from .09 to .00. The body of the table contains the cumulative probabilities corresponding to each Z-score value and its associated hundredth place decimal.#### Example Row:For Z = -3.4:- .09: 0.0002- .08: 0.0003- .07: 0.0003- .06: 0.0003- .05: 0.0003- .04: 0.0003- .03: 0.0003- .02: 0.0003- .01: 0.0003- .00: 0.0003#### Further Details:For Z = -2.5:- .09: 0.0064- .08: 0.0070- .07: 0.0078- .06: 0.0087- .05: 0.0096- .04: 0.0107- .03: 0.0119- .02: 0.0132- .01: 0.0146- .00: 0.0160This table helps in determining the likelihood that a random variable falls below a particular Z-score in a standard normal distribution. For more precise probabilities, users refer to the row for the closest Z-score and the column matching the hundredths decimal place. The image contains a standard normal distribution (Z-score) table. This table shows the cumulative probability of a standard normal distribution up to a given Z-score. The leftmost column represents the integer part and the first decimal place of the Z-score, while the topmost row represents the second decimal place. The intersection of the row and column gives the cumulative probability.### Table Layout:- **Z-Score (Row):** Starts from 0.0 to 2.0, increasing in increments of 0.1.- **Decimal Places (Column):** Additional decimal values from .00 to .09.### Example Interpretation:- If the Z-score is 0.0, the cumulative probability is 0.5000.- For a Z-score of 1.27, you go to the row starting with 1.2 and the column .07 to find 0.8980, which is the cumulative probability.This table is typically used in statistics to determine the probability that a standard normal random variable is less than or equal to a given value, essential in hypothesis testing and confidence interval calculations.

Normal distribution is also known as the Gaussian distribution. It is very useful in statistics.

Answered: Find the indicated probability using…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Find the indicated probability using the standard normal distribution. P(0 < z < 0.535) P ( 0 < z < 0.535) =

The image displays a portion of a standard normal distribution table, commonly used in statistics to find the probability associated with a given Z-score. This table typically shows the cumulative probability of a standard normal distribution (mean = 0, standard deviation = 1).

### Transcription of the Table:

The Z-score values range from -3.4 to -1.4 along the leftmost column, and the probabilities for each hundredth place are provided across the top row, from .09 to .00. The body of the table contains the cumulative probabilities corresponding to each Z-score value and its associated hundredth place decimal.

#### Example Row:
For Z = -3.4:
- .09: 0.0002
- .08: 0.0003
- .07: 0.0003
- .06: 0.0003
- .05: 0.0003
- .04: 0.0003
- .03: 0.0003
- .02: 0.0003
- .01: 0.0003
- .00: 0.0003

#### Further Details:
For Z = -2.5:
- .09: 0.0064
- .08: 0.0070
- .07: 0.0078
- .06: 0.0087
- .05: 0.0096
- .04: 0.0107
- .03: 0.0119
- .02: 0.0132
- .01: 0.0146
- .00: 0.0160

This table helps in determining the likelihood that a random variable falls below a particular Z-score in a standard normal distribution. For more precise probabilities, users refer to the row for the closest Z-score and the column matching the hundredths decimal place.

The image contains a standard normal distribution (Z-score) table. This table shows the cumulative probability of a standard normal distribution up to a given Z-score. The leftmost column represents the integer part and the first decimal place of the Z-score, while the topmost row represents the second decimal place. The intersection of the row and column gives the cumulative probability.

### Table Layout:

- **Z-Score (Row):** Starts from 0.0 to 2.0, increasing in increments of 0.1.
- **Decimal Places (Column):** Additional decimal values from .00 to .09.

### Example Interpretation:

- If the Z-score is 0.0, the cumulative probability is 0.5000.
- For a Z-score of 1.27, you go to the row starting with 1.2 and the column .07 to find 0.8980, which is the cumulative probability.

This table is typically used in statistics to determine the probability that a standard normal random variable is less than or equal to a given value, essential in hypothesis testing and confidence interval calculations.

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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