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the probability that a randomly selected bag contains fewer than 1025 chocolate chips? oportion of bags contains more than 1200 chocolate chips? the percentile rank of a bag that contains 1025 chocolate chips? ables of Areas under the Normal Curve Standard Normal Distribution z .00 .01 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 <-33 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 <-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 <-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 00011 0.0011 0.0010 0.0010 -29 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 <-28 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 .02 .03 .04 .05 .06 .07 .08 .09 - X

the probability that a randomly selected bag contains fewer than 1025 chocolate chips? oportion of bags contains more than 1200 chocolate chips? the percentile rank of a bag that contains 1025 chocolate chips? ables of Areas under the Normal Curve Standard Normal Distribution z .00 .01 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 <-33 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 <-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 <-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 00011 0.0011 0.0010 0.0010 -29 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 <-28 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 .02 .03 .04 .05 .06 .07 .08 .09 - X

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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**Tables of Areas under the Normal Curve** The table presented shows the cumulative areas (probabilities) under the standard normal distribution curve. It is used to find the probability that a statistic is less than a given z-score. The rows represent the first decimal of the z-score, and the columns represent the second decimal place. ### Detailed Explanation: - **Z-Score Values:** - The leftmost column contains z-score values ranging from -0.5 to 3.4 in increments of 0.1. - For each row, the z-score is the sum of the row and column headers. - **Area Values:** - Each cell within the table represents the area under the normal curve to the left of the specified z-score. - For example, if you look at a z-score of 0.5 (row) and 0.03 (column), you locate the intersection which gives you the cumulative area/probability. - **Columns:** - Columns are labeled from 0.00 to 0.09, representing the second decimal place of z-scores. This table is essential in statistics for determining probabilities in standard normal distribution problems, useful in fields such as psychology, business, and the natural and social sciences.
Transcribed Image Text:**Tables of Areas under the Normal Curve** The table presented shows the cumulative areas (probabilities) under the standard normal distribution curve. It is used to find the probability that a statistic is less than a given z-score. The rows represent the first decimal of the z-score, and the columns represent the second decimal place. ### Detailed Explanation: - **Z-Score Values:** - The leftmost column contains z-score values ranging from -0.5 to 3.4 in increments of 0.1. - For each row, the z-score is the sum of the row and column headers. - **Area Values:** - Each cell within the table represents the area under the normal curve to the left of the specified z-score. - For example, if you look at a z-score of 0.5 (row) and 0.03 (column), you locate the intersection which gives you the cumulative area/probability. - **Columns:** - Columns are labeled from 0.00 to 0.09, representing the second decimal place of z-scores. This table is essential in statistics for determining probabilities in standard normal distribution problems, useful in fields such as psychology, business, and the natural and social sciences.
### Normal Distribution and Probability **Problem Statement:** The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 and a standard deviation of 129 chips. 1. **(a)** What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? 2. **(b)** What is the probability that a randomly selected bag contains fewer than 1025 chocolate chips? 3. **(c)** What proportion of bags contains more than 1200 chocolate chips? 4. **(d)** What is the percentile rank of a bag that contains 1025 chocolate chips? --- ### Explanation of Diagrams and Tables: **Diagram:** - **Graph:** The graph on the left is a standard normal distribution curve (bell curve). It typically represents data that clusters around a mean. - **Area:** The shaded area under the curve represents the probability related to specific z-scores. **Table of Areas under the Normal Curve:** - **Table Layout:** The table provides the cumulative area (probability) from the left up to a z-score. - **Columns:** Represent the decimal part of the z-score. - **Rows:** Represent the whole number and tenths of the z-score. - **How to Use:** - Find the z-score at the intersection of the corresponding row and column to determine the cumulative probability. The table is used to calculate the probability of a random variable falling within a particular range under the normal distribution curve. This is crucial when solving problems related to normal distributions in statistics. --- This content explains how to use the standard normal distribution to solve real-world probability problems, focusing on examples involving normally distributed data.
Transcribed Image Text:### Normal Distribution and Probability **Problem Statement:** The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 and a standard deviation of 129 chips. 1. **(a)** What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? 2. **(b)** What is the probability that a randomly selected bag contains fewer than 1025 chocolate chips? 3. **(c)** What proportion of bags contains more than 1200 chocolate chips? 4. **(d)** What is the percentile rank of a bag that contains 1025 chocolate chips? --- ### Explanation of Diagrams and Tables: **Diagram:** - **Graph:** The graph on the left is a standard normal distribution curve (bell curve). It typically represents data that clusters around a mean. - **Area:** The shaded area under the curve represents the probability related to specific z-scores. **Table of Areas under the Normal Curve:** - **Table Layout:** The table provides the cumulative area (probability) from the left up to a z-score. - **Columns:** Represent the decimal part of the z-score. - **Rows:** Represent the whole number and tenths of the z-score. - **How to Use:** - Find the z-score at the intersection of the corresponding row and column to determine the cumulative probability. The table is used to calculate the probability of a random variable falling within a particular range under the normal distribution curve. This is crucial when solving problems related to normal distributions in statistics. --- This content explains how to use the standard normal distribution to solve real-world probability problems, focusing on examples involving normally distributed data.
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