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Suppose the people living in a city have a mean score of 36 and a standard deviation of 3 on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the 50% -34% -14% figures, what is the minimum score a person has to have to be in the top (a) 2%, (b) 16%, (c) 50%, (d) 84%, and (e) 98%?

Suppose the people living in a city have a mean score of 36 and a standard deviation of 3 on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the 50% -34% -14% figures, what is the minimum score a person has to have to be in the top (a) 2%, (b) 16%, (c) 50%, (d) 84%, and (e) 98%?

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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**Transcribed Text:** Suppose the people living in a city have a mean score of 36 and a standard deviation of 3 on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the 50% – 34% – 14% figures, what is the minimum score a person has to have to be in the top (a) 2%, (b) 16%, (c) 50%, (d) 84%, and (e) 98%? --- **Explanation for an Educational Website:** This problem involves understanding normal distribution and calculating z-scores to find the minimum scores corresponding to certain percentiles. 1. **Normal Distribution:** A type of continuous probability distribution for a real-valued random variable. It is often referred to as the bell curve because of its shape. 2. **Mean:** The average score of the group, which is 36 in this instance. 3. **Standard Deviation:** A measure of the amount of variation or dispersion of a set of values, which is 3 here. 4. **Percentiles:** The question asks for the minimum score needed to be at different percentile ranks: 2%, 16%, 50%, 84%, and 98%. 5. **Z-scores:** Used to determine the score corresponding to each percentile. A z-score tells us how many standard deviations an element is from the mean. 6. **The 50% – 34% – 14% Rule:** This is a simplified reference to the empirical rule in statistics, stating that approximately: - 68% of values fall within one standard deviation of the mean. - 95% fall within two standard deviations. - 99.7% fall within three standard deviations. Using this information, you can calculate the specific scores that correspond to the given percentile thresholds by using statistical z-tables or calculations.
Transcribed Image Text:**Transcribed Text:** Suppose the people living in a city have a mean score of 36 and a standard deviation of 3 on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the 50% – 34% – 14% figures, what is the minimum score a person has to have to be in the top (a) 2%, (b) 16%, (c) 50%, (d) 84%, and (e) 98%? --- **Explanation for an Educational Website:** This problem involves understanding normal distribution and calculating z-scores to find the minimum scores corresponding to certain percentiles. 1. **Normal Distribution:** A type of continuous probability distribution for a real-valued random variable. It is often referred to as the bell curve because of its shape. 2. **Mean:** The average score of the group, which is 36 in this instance. 3. **Standard Deviation:** A measure of the amount of variation or dispersion of a set of values, which is 3 here. 4. **Percentiles:** The question asks for the minimum score needed to be at different percentile ranks: 2%, 16%, 50%, 84%, and 98%. 5. **Z-scores:** Used to determine the score corresponding to each percentile. A z-score tells us how many standard deviations an element is from the mean. 6. **The 50% – 34% – 14% Rule:** This is a simplified reference to the empirical rule in statistics, stating that approximately: - 68% of values fall within one standard deviation of the mean. - 95% fall within two standard deviations. - 99.7% fall within three standard deviations. Using this information, you can calculate the specific scores that correspond to the given percentile thresholds by using statistical z-tables or calculations.
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