W#1 NOTE Normal & Standard Normal Probability Distribution Part 1

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School

Fairleigh Dickinson University *

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Course

2023

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Business

Date

Feb 20, 2024

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docx

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Uploaded by mlle445

W#1 NOTE Normal & Standard Normal Probability Distribution Part 1 A normal curve is symmetrically bell-shaped, and is centered about the mean, median and mode for a continuous probability distribution. - Agree The standard normal or z curve is a special case of the normal distribution with mean one (1) and standard deviation zero (0) . - Disagree Let's try again. The standard normal or z curve is a special case of the normal distribution with mean zero (0) and standard deviation one (1) . - Agree

The total area under any normal or standard normal probability curve equals one ( 1 ) because it represents 100% of all the possible outcomes for that distribution. - Agree What is the chance a data value from a normally distributed random variable is located or positioned below the mean? Express the answer as a whole percentage with percent symbol. - 50% What is the chance a data value from a normally distributed random variable is located or positioned above the mean? Express the answer as a whole percentage with percent symbol. - 50% According to the Empirical Rule , what percentage of normally distributed data is located or positioned within one (1) standard deviation of the mean? Express the answer as a percentage to the hundredths place. - 68.27% According to the Empirical Rule , what percentage of normally distributed data is located or positioned within two (2) standard deviations of the mean? Express the answer as a percentage to the hundredths place. - 95.45% According to the Empirical Rule , what percentage of normally distributed data is located or positioned within three (3) standard deviations of the mean? Express the answer as a percentage to the hundredths place. - 99.73% A standard normal or z-score is a measure of location and position. This is an example of a third such data measure, after measures of central tendency, such as the mean, and variability, such as the range - Agree A z-score or standardized score for a normally distributed random variable, x , is calculated according to the following formula:

- A = data value, x - B = mean value : for sample,  for population - C = standard deviation : s for sample, or  for population - D = z-score or standardized score Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the z-score equivalent to a test score of 480? - 1 Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the z-score equivalent to a test score of 320? - -1 Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the approximate chance the test taker had a score between 320 and 480? - 68% Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They

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prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the z-score equivalent to a test score of 560? - 2 Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the z-score equivalent to a test score of 240? - -2 They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the approximate chance the test taker had a score between 240 and 560? - 95% Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the z-score equivalent to a test score of 640? - 3 Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol.

What is the z-score equivalent to a test score of 160? - -3 Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the approximate chance the test taker had a score between 160 and 640? - 100% Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the approximate chance the test taker had a score between 400 and 560? - 48%* Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the approximate chance the test taker had a score between 240 and 400? - 48%* Colin and Colleen work for Acme Assessments. They have devised a new standardized testing instrument that assesses comprehensive career communication competencies. The product is designed with the following norms: the scores follow a normal distribution with a (population) mean average score of 400 and a (population) standard deviation of 80. They prepare to select randomly a test taken by a subject during the pilot study. Estimate the following probabilities, utilizing the Empirical Rule : Round only the final percentages to the nearest whole percent, stating the answer with percent symbol. What is the approximate chance the test taker had a score between 160 and 480? - 84%**

* = 68.27 2 + 95.45 − 68.27 2 = 34.135 + 13.59 = 47.725 ** = 68.27 + 13.59 + 2.5 = 84.36%

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W#1 NOTE Normal & Standard Normal Probability Distribution Part 1

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