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 Part C Only!!

A television sports commentator wants to estimate the proportion of citizens who "follow professional football." Complete parts (a) through (c). **Links to Standard Normal Distribution Tables:** - Click here to view the standard normal distribution table (page 1). - Click here to view the standard normal distribution table (page 2). --- **(a)** What sample size should be obtained if he wants to be within 2 percentage points with 94% confidence if he uses an estimate of 48% obtained from a poll? The sample size is **2206**. (Round up to the nearest integer.) **(b)** What sample size should be obtained if he wants to be within 2 percentage points with 94% confidence if he does not use any prior estimates? The sample size is **2211**. (Round up to the nearest integer.) **(c)** Why are the results from parts (a) and (b) so close? - **A.** The results are close because the confidence 94% is close to 100%. - **B.** The results are close because 0.48(1 − 0.48) = 0.2496 is very close to 0.25. - **C.** The results are close because the margin of error 2% is less than 5%.
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Transcribed Image Text:A television sports commentator wants to estimate the proportion of citizens who "follow professional football." Complete parts (a) through (c). **Links to Standard Normal Distribution Tables:** - Click here to view the standard normal distribution table (page 1). - Click here to view the standard normal distribution table (page 2). --- **(a)** What sample size should be obtained if he wants to be within 2 percentage points with 94% confidence if he uses an estimate of 48% obtained from a poll? The sample size is **2206**. (Round up to the nearest integer.) **(b)** What sample size should be obtained if he wants to be within 2 percentage points with 94% confidence if he does not use any prior estimates? The sample size is **2211**. (Round up to the nearest integer.) **(c)** Why are the results from parts (a) and (b) so close? - **A.** The results are close because the confidence 94% is close to 100%. - **B.** The results are close because 0.48(1 − 0.48) = 0.2496 is very close to 0.25. - **C.** The results are close because the margin of error 2% is less than 5%.
# Standard Normal Distribution Table ## Page 1 ### Graph Explanation The graph presented at the top of the page is a standard normal distribution curve, which is bell-shaped and symmetrical around the mean (zero). The shaded area represents the probability to the left of the given z-value. The vertical line intercepting the x-axis indicates a specific z-value, z, on the distribution. ### Standard Normal Distribution Table The table lists z-values ranging from -3.4 to -0.1 along the leftmost column. The upper row of the table indicates the decimal value (0.00 to 0.09) to add to the z-value from the leftmost column. The intersection of a row z-value and a column decimal value provides the proportion of the standard normal distribution curve to the left of that combined z-value. For example: - z = -3.4, additional 0.00: Probability = 0.0003 - z = -2.5, additional 0.06: Probability = 0.0062 ## Page 2 ### Graph Explanation Similar to page 1, this graph shows another view of the standard normal distribution, emphasizing the shaded area (probability) to the left of a given z-value, z. ### Standard Normal Distribution Table The table continues from where page 1 ends, listing z-values ranging from 0.0 to 2.9. The leftmost column contains these z-values, and the top row represents the decimal additions (0.00 to 0.09). The table cells give the cumulative probability from the left up to the specified z-value. For example: - z = 0.0, additional 0.02: Probability = 0.5080 - z = 1.7, additional 0.04: Probability = 0.9582 This table is crucial for statistical calculations, often used to find probabilities and percentiles in a normal distribution.
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Transcribed Image Text:# Standard Normal Distribution Table ## Page 1 ### Graph Explanation The graph presented at the top of the page is a standard normal distribution curve, which is bell-shaped and symmetrical around the mean (zero). The shaded area represents the probability to the left of the given z-value. The vertical line intercepting the x-axis indicates a specific z-value, z, on the distribution. ### Standard Normal Distribution Table The table lists z-values ranging from -3.4 to -0.1 along the leftmost column. The upper row of the table indicates the decimal value (0.00 to 0.09) to add to the z-value from the leftmost column. The intersection of a row z-value and a column decimal value provides the proportion of the standard normal distribution curve to the left of that combined z-value. For example: - z = -3.4, additional 0.00: Probability = 0.0003 - z = -2.5, additional 0.06: Probability = 0.0062 ## Page 2 ### Graph Explanation Similar to page 1, this graph shows another view of the standard normal distribution, emphasizing the shaded area (probability) to the left of a given z-value, z. ### Standard Normal Distribution Table The table continues from where page 1 ends, listing z-values ranging from 0.0 to 2.9. The leftmost column contains these z-values, and the top row represents the decimal additions (0.00 to 0.09). The table cells give the cumulative probability from the left up to the specified z-value. For example: - z = 0.0, additional 0.02: Probability = 0.5080 - z = 1.7, additional 0.04: Probability = 0.9582 This table is crucial for statistical calculations, often used to find probabilities and percentiles in a normal distribution.
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