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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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**Standard Normal Probabilities Table** This table provides the probabilities associated with the standard normal distribution, represented by Z-scores. The Z-scores are shown along the left column, and the probabilities are displayed across the top header. Each cell within the table represents the cumulative probability for a given Z-score value. ### Structure: - **Z-Score Values**: These are listed on the left side ranging from -3.4 to 3.4 in increments of 0.1. - **Probabilities**: The top row represents the second decimal place of the Z-score (from .00 to .09). ### Example of Use: - To find the probability of a Z-score of -2.3: - Locate -2.3 in the leftmost column. - Move across the row to the column labeled with your desired decimal (e.g., .04 for -2.34). - The intersection provides the probability (e.g., 0.0094 for Z = -2.34). This table is essential for statistical calculations, used to determine the probability of a random variable falling below a specific Z-score in a standard normal distribution. **Note**: The probabilities represent the area under the curve to the left of the Z-score in a standard normal distribution graph, which is symmetrical around 0.
Transcribed Image Text:**Standard Normal Probabilities Table** This table provides the probabilities associated with the standard normal distribution, represented by Z-scores. The Z-scores are shown along the left column, and the probabilities are displayed across the top header. Each cell within the table represents the cumulative probability for a given Z-score value. ### Structure: - **Z-Score Values**: These are listed on the left side ranging from -3.4 to 3.4 in increments of 0.1. - **Probabilities**: The top row represents the second decimal place of the Z-score (from .00 to .09). ### Example of Use: - To find the probability of a Z-score of -2.3: - Locate -2.3 in the leftmost column. - Move across the row to the column labeled with your desired decimal (e.g., .04 for -2.34). - The intersection provides the probability (e.g., 0.0094 for Z = -2.34). This table is essential for statistical calculations, used to determine the probability of a random variable falling below a specific Z-score in a standard normal distribution. **Note**: The probabilities represent the area under the curve to the left of the Z-score in a standard normal distribution graph, which is symmetrical around 0.
# Educational Content on Sampling Distribution ## Topic: Understanding Sampling Distribution and Probability ### Scenario A government sample survey aims to measure the blood cholesterol level of a Simple Random Sample (SRS) of men aged 20 to 34. The cholesterol levels follow a Normal distribution with a mean (\( \mu \)) of 186 milligrams per deciliter (mg/dl) and a standard deviation (\( s \)) of 41 mg/dl. ### Step-by-Step Guide #### Step 1: Determine the Sampling Distribution Choose an SRS of 100 men from this population. - **Question:** What is the sampling distribution of \( \overline{x} \)? (Use the units of mg/dl.) - \( N(186, 0.41) \) distribution. - \( N(186, 41) \) distribution. - \( N(1.86, 0.41) \) distribution. - \( N(186, 4.1) \) distribution. #### Step 2: Calculating Probability Find the probability that \( \overline{x} \) takes a value between 183 and 189 mg/dl. This is the probability that \( \overline{x} \) estimates \( \mu \) within ±3 mg/dl. - **Choices:** - 0.6800 - 0.5346 - 0.2327 - 0.4654 #### Step 3: Sampling with a Larger Sample Size Choose an SRS of 1000 men from this population. Determine the probability that \( \overline{x} \) falls within ±3 mg/dl of \( \mu \). - Utilize **Table A** to provide an answer rounded to three decimal places. This exercise helps understand the concept of sampling distribution and the use of Normal distribution to find probabilities in biological statistics.
Transcribed Image Text:# Educational Content on Sampling Distribution ## Topic: Understanding Sampling Distribution and Probability ### Scenario A government sample survey aims to measure the blood cholesterol level of a Simple Random Sample (SRS) of men aged 20 to 34. The cholesterol levels follow a Normal distribution with a mean (\( \mu \)) of 186 milligrams per deciliter (mg/dl) and a standard deviation (\( s \)) of 41 mg/dl. ### Step-by-Step Guide #### Step 1: Determine the Sampling Distribution Choose an SRS of 100 men from this population. - **Question:** What is the sampling distribution of \( \overline{x} \)? (Use the units of mg/dl.) - \( N(186, 0.41) \) distribution. - \( N(186, 41) \) distribution. - \( N(1.86, 0.41) \) distribution. - \( N(186, 4.1) \) distribution. #### Step 2: Calculating Probability Find the probability that \( \overline{x} \) takes a value between 183 and 189 mg/dl. This is the probability that \( \overline{x} \) estimates \( \mu \) within ±3 mg/dl. - **Choices:** - 0.6800 - 0.5346 - 0.2327 - 0.4654 #### Step 3: Sampling with a Larger Sample Size Choose an SRS of 1000 men from this population. Determine the probability that \( \overline{x} \) falls within ±3 mg/dl of \( \mu \). - Utilize **Table A** to provide an answer rounded to three decimal places. This exercise helps understand the concept of sampling distribution and the use of Normal distribution to find probabilities in biological statistics.
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