MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Answer parts A and C Only!

**Standard Normal Distribution Table** The standard normal distribution is a key concept in statistics, representing a normal distribution with a mean of 0 and a standard deviation of 1. This table, often used in statistical analysis, provides the area (probability) to the left of a given z-score in a standard normal distribution. ### Explanation of Graphs In both pages, a bell-shaped curve represents the standard normal distribution. The curve is symmetrical about the mean (z = 0). The shaded region to the left of a particular z-value represents the cumulative probability up to that z-value. The "Area" refers to this cumulative probability. ### Standard Normal Distribution Table (Page 1) This table provides values of cumulative probabilities for negative z-scores from -3.4 to -0.1. The z-values are listed in the first column, with the first decimal place of the z-value across the top representing additional decimal places (0.00 to 0.09). For example: - For z = -2.5, the cumulative probability from the table is 0.0062. ### Standard Normal Distribution Table (Page 2) This table displays values for positive z-scores from 0.0 to 3.4. Similar to page 1, the first column lists the z-scores, with additional decimal places across the top. For example: - For z = 1.5, the cumulative probability from the table is 0.9332. These tables are crucial tools for finding probabilities and percentiles in data that follow a standard normal distribution.
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Transcribed Image Text:**Standard Normal Distribution Table** The standard normal distribution is a key concept in statistics, representing a normal distribution with a mean of 0 and a standard deviation of 1. This table, often used in statistical analysis, provides the area (probability) to the left of a given z-score in a standard normal distribution. ### Explanation of Graphs In both pages, a bell-shaped curve represents the standard normal distribution. The curve is symmetrical about the mean (z = 0). The shaded region to the left of a particular z-value represents the cumulative probability up to that z-value. The "Area" refers to this cumulative probability. ### Standard Normal Distribution Table (Page 1) This table provides values of cumulative probabilities for negative z-scores from -3.4 to -0.1. The z-values are listed in the first column, with the first decimal place of the z-value across the top representing additional decimal places (0.00 to 0.09). For example: - For z = -2.5, the cumulative probability from the table is 0.0062. ### Standard Normal Distribution Table (Page 2) This table displays values for positive z-scores from 0.0 to 3.4. Similar to page 1, the first column lists the z-scores, with additional decimal places across the top. For example: - For z = 1.5, the cumulative probability from the table is 0.9332. These tables are crucial tools for finding probabilities and percentiles in data that follow a standard normal distribution.
Suppose a simple random sample of size \( n = 125 \) is obtained from a population whose size is \( N = 25,000 \) and whose population proportion with a specified characteristic is \( p = 0.2 \). [Click here to view the standard normal distribution table (page 1).] [Click here to view the standard normal distribution table (page 2).] --- **(a) Describe the sampling distribution of \( \hat{p} \).** Choose the phrase that best describes the shape of the sampling distribution below. - A. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \). - B. Not normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \). - C. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \). - D. Not normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \). **Determine the mean of the sampling distribution of \( \hat{p} \).** \( \mu_{\hat{p}} = 0.2 \) (Round to one decimal place as needed.) **Determine the standard deviation of the sampling distribution of \( \hat{p} \).** \( \sigma_{\hat{p}} = 0.035777 \) (Round to six decimal places as needed.) --- **(b) What is the probability of obtaining \( x = 30 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.24) \)?** \( P(\hat{p} \geq 0.24) = 0.1318 \) (Round to four decimal places as needed.) --- **(c) What is the probability of obtaining \( x = 15 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.12) \)?** \( P(\hat{p} \leq 0.12) = \) [ ] (Round to four decimal places as needed.)
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Transcribed Image Text:Suppose a simple random sample of size \( n = 125 \) is obtained from a population whose size is \( N = 25,000 \) and whose population proportion with a specified characteristic is \( p = 0.2 \). [Click here to view the standard normal distribution table (page 1).] [Click here to view the standard normal distribution table (page 2).] --- **(a) Describe the sampling distribution of \( \hat{p} \).** Choose the phrase that best describes the shape of the sampling distribution below. - A. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \). - B. Not normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \). - C. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \). - D. Not normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \). **Determine the mean of the sampling distribution of \( \hat{p} \).** \( \mu_{\hat{p}} = 0.2 \) (Round to one decimal place as needed.) **Determine the standard deviation of the sampling distribution of \( \hat{p} \).** \( \sigma_{\hat{p}} = 0.035777 \) (Round to six decimal places as needed.) --- **(b) What is the probability of obtaining \( x = 30 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.24) \)?** \( P(\hat{p} \geq 0.24) = 0.1318 \) (Round to four decimal places as needed.) --- **(c) What is the probability of obtaining \( x = 15 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.12) \)?** \( P(\hat{p} \leq 0.12) = \) [ ] (Round to four decimal places as needed.)
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n=125

p=0.2

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