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(a) The area to the right of Z = - 0.12 is (Round to four decimal places as needed.) (b) The area to the right of Z= 0.53 is (Round to four decimal places as needed.) (c) The area to the right of Z= - 1.36 is (Round to four decimal places as needed.)

(a) The area to the right of Z = - 0.12 is (Round to four decimal places as needed.) (b) The area to the right of Z= 0.53 is (Round to four decimal places as needed.) (c) The area to the right of Z= - 1.36 is (Round to four decimal places as needed.)

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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Determine the area under the standard normal curve that lies to the right of (a) Z = -0.12, (b) Z = 0.53, (c) Z = -1.36, and (d) Z = 1.53. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) The area to the right of Z = -0.12 is [ ]. (Round to four decimal places as needed.) (b) The area to the right of Z = 0.53 is [ ]. (Round to four decimal places as needed.) (c) The area to the right of Z = -1.36 is [ ]. (Round to four decimal places as needed.) (d) The area to the right of Z = 1.53 is [ ]. (Round to four decimal places as needed.)
Transcribed Image Text:Determine the area under the standard normal curve that lies to the right of (a) Z = -0.12, (b) Z = 0.53, (c) Z = -1.36, and (d) Z = 1.53. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) The area to the right of Z = -0.12 is [ ]. (Round to four decimal places as needed.) (b) The area to the right of Z = 0.53 is [ ]. (Round to four decimal places as needed.) (c) The area to the right of Z = -1.36 is [ ]. (Round to four decimal places as needed.) (d) The area to the right of Z = 1.53 is [ ]. (Round to four decimal places as needed.)
## Introduction to the Standard Normal Distribution The standard normal distribution is a fundamental concept in statistics representing a normal distribution with a mean of 0 and a standard deviation of 1. This distribution is often used in hypothesis testing and statistics in general to assess probabilities and interpret Z-scores. ### Explanation of Z-Score Table The images provided contain a standard normal distribution table. This table shows areas (probabilities) corresponding to Z-scores, which represent the number of standard deviations a data point is from the mean. #### Left Side of the Image - **Diagram**: A bell curve with a shaded area to the left of the Z-score (\( z \)). This represents the cumulative probability of a value being less than the given Z-score. - **Table**: This part of the table lists the cumulative probabilities for negative Z-scores ranging from -3.4 to 0. The table is read by combining the Z-score value from the column with the thousandth value from the row. #### Right Side of the Image - **Diagram**: Similar to the first, this diagram shows the bell curve with a shaded area, again corresponding to the cumulative probability up to Z-score \( z \). - **Table**: This section covers Z-scores from 0 to 3.0. The structure of reading the table remains the same. For example, a Z-score of 0.53 would be found by intersecting the row for 0.5 and the column for 0.03. ### How to Use the Table 1. **Identify the Z-Score**: Determine the Z-score you need by using the formula \( Z = \frac{(X - \mu)}{\sigma} \), where \( X \) is your data point, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. 2. **Locate the Row and Column**: For a Z-score of 1.25, for example, find the row labeled "1.2" and the column labeled ".05". 3. **Find the Probability**: The intersecting value is the cumulative probability \( P(Z \leq z) \). ### Applications Standard normal distribution tables are extensively used in: - **Confidence Intervals**: Calculating the probability and establishing intervals. - **Hypothesis Testing**: Determining p-values for statistical tests. - **Quality Control**: Assessing process deviations
Transcribed Image Text:## Introduction to the Standard Normal Distribution The standard normal distribution is a fundamental concept in statistics representing a normal distribution with a mean of 0 and a standard deviation of 1. This distribution is often used in hypothesis testing and statistics in general to assess probabilities and interpret Z-scores. ### Explanation of Z-Score Table The images provided contain a standard normal distribution table. This table shows areas (probabilities) corresponding to Z-scores, which represent the number of standard deviations a data point is from the mean. #### Left Side of the Image - **Diagram**: A bell curve with a shaded area to the left of the Z-score (\( z \)). This represents the cumulative probability of a value being less than the given Z-score. - **Table**: This part of the table lists the cumulative probabilities for negative Z-scores ranging from -3.4 to 0. The table is read by combining the Z-score value from the column with the thousandth value from the row. #### Right Side of the Image - **Diagram**: Similar to the first, this diagram shows the bell curve with a shaded area, again corresponding to the cumulative probability up to Z-score \( z \). - **Table**: This section covers Z-scores from 0 to 3.0. The structure of reading the table remains the same. For example, a Z-score of 0.53 would be found by intersecting the row for 0.5 and the column for 0.03. ### How to Use the Table 1. **Identify the Z-Score**: Determine the Z-score you need by using the formula \( Z = \frac{(X - \mu)}{\sigma} \), where \( X \) is your data point, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. 2. **Locate the Row and Column**: For a Z-score of 1.25, for example, find the row labeled "1.2" and the column labeled ".05". 3. **Find the Probability**: The intersecting value is the cumulative probability \( P(Z \leq z) \). ### Applications Standard normal distribution tables are extensively used in: - **Confidence Intervals**: Calculating the probability and establishing intervals. - **Hypothesis Testing**: Determining p-values for statistical tests. - **Quality Control**: Assessing process deviations
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