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Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probabilities. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four B decimal places. Part: 0/2 Part 1 of 2 (a) A randomly selected teacher earns between $38.500 and $50,000 a year. P (38,500 ≤x≤ 50,000) =

Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probabilities. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four B decimal places. Part: 0/2 Part 1 of 2 (a) A randomly selected teacher earns between $38.500 and $50,000 a year. P (38,500 ≤x≤ 50,000) =

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Topic: Understanding Statistical Distributions** **Teachers' Salaries** The average annual salary for all U.S. teachers is $47,750. Assuming that the distribution is normal and the standard deviation is $5680, find the probabilities. **Instructions:** 1. Use a TI-83 Plus/TI-84 Plus calculator. 2. Round the answer to at least four decimal places. ### Problem Statement: **Part 1:** - **Problem:** A randomly selected teacher earns between $38,500 and $50,000 a year. - **Notation:** \( P(38,500 \leq X \leq 50,000) = \) Use the mean (\(\mu = 47,750\)) and standard deviation (\(\sigma = 5680\)) values provided to solve the probability using the appropriate statistical functions on the TI-83 Plus/TI-84 Plus calculator. ### Instructions on Using TI-83 Plus/TI-84 Plus Calculator: 1. **Turn on the calculator.** 2. **Press 2nd.** 3. **Press VARS (to access the DISTR menu).** 4. **Select normalCDF( function.** In the normalCDF function, input the lower bound, upper bound, mean, and standard deviation as follows: ``` normalCDF(lower bound, upper bound, mean, standard deviation) normalCDF(38500, 50000, 47750, 5680) ``` 5. **Press ENTER to calculate the probability.** This probability represents the likelihood that a randomly selected teacher's salary falls within the given range. Note: Please refer to your calculator manual or online resources if you encounter any difficulties operating the functions. **End of Instructions Chain** --- Ensure that each step is followed accurately for precise results. If you have any questions or require further assistance, please consult your instructor or the calculator manual.
Transcribed Image Text:**Topic: Understanding Statistical Distributions** **Teachers' Salaries** The average annual salary for all U.S. teachers is $47,750. Assuming that the distribution is normal and the standard deviation is $5680, find the probabilities. **Instructions:** 1. Use a TI-83 Plus/TI-84 Plus calculator. 2. Round the answer to at least four decimal places. ### Problem Statement: **Part 1:** - **Problem:** A randomly selected teacher earns between $38,500 and $50,000 a year. - **Notation:** \( P(38,500 \leq X \leq 50,000) = \) Use the mean (\(\mu = 47,750\)) and standard deviation (\(\sigma = 5680\)) values provided to solve the probability using the appropriate statistical functions on the TI-83 Plus/TI-84 Plus calculator. ### Instructions on Using TI-83 Plus/TI-84 Plus Calculator: 1. **Turn on the calculator.** 2. **Press 2nd.** 3. **Press VARS (to access the DISTR menu).** 4. **Select normalCDF( function.** In the normalCDF function, input the lower bound, upper bound, mean, and standard deviation as follows: ``` normalCDF(lower bound, upper bound, mean, standard deviation) normalCDF(38500, 50000, 47750, 5680) ``` 5. **Press ENTER to calculate the probability.** This probability represents the likelihood that a randomly selected teacher's salary falls within the given range. Note: Please refer to your calculator manual or online resources if you encounter any difficulties operating the functions. **End of Instructions Chain** --- Ensure that each step is followed accurately for precise results. If you have any questions or require further assistance, please consult your instructor or the calculator manual.
**Title: Understanding Z-scores and the Area Under the Normal Distribution Curve** **Introduction:** In statistics, the Z-score represents the number of standard deviations a data point is from the mean. Understanding how to find the Z-value corresponding to a given area under a normal distribution curve is essential for interpreting and analyzing data. **Example Problem:** *Find the Z value that corresponds to the given area in the figure below. Use a graphing calculator and round the answer to four decimal places.* **Diagram Explanation:** The diagram illustrates a normal distribution curve, which is bell-shaped and symmetric about the mean (µ = 0). It shows an area under the curve corresponding to the Z value we need to find. The shaded area under the curve to the left of a vertical line is labeled with the value 0.5999. This represents the cumulative area from the far left tail to the Z value. **Steps to Solve:** 1. **Graphical Representation:** - Identify the shaded area, which indicates the cumulative probability (area to the left of the Z value). 2. **Using a Graphing Calculator:** - To find the Z value corresponding to the cumulative area of 0.5999, use the inverse normal distribution function on the calculator. - Input 0.5999 as the cumulative probability to retrieve the corresponding Z value. 3. **Round to Four Decimal Places:** - Once the Z value is found, round it to four decimal places for precision. **Student Practice:** **Example Calculation:** - Given cumulative area: 0.5999 - Using a graphing calculator or Z-table, find the corresponding Z value. - The process will yield an approximate Z value, which students should then round to four decimal places. **Answer Submission:** - Students will input their Z value into the provided field and submit their answers for evaluation. **Conclusion:** Understanding how to calculate Z values from given areas is crucial in statistics for interpreting probabilities and making data-driven decisions. Practice with various cumulative areas to become proficient at using normal distribution curves and Z-scores. © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center
Transcribed Image Text:**Title: Understanding Z-scores and the Area Under the Normal Distribution Curve** **Introduction:** In statistics, the Z-score represents the number of standard deviations a data point is from the mean. Understanding how to find the Z-value corresponding to a given area under a normal distribution curve is essential for interpreting and analyzing data. **Example Problem:** *Find the Z value that corresponds to the given area in the figure below. Use a graphing calculator and round the answer to four decimal places.* **Diagram Explanation:** The diagram illustrates a normal distribution curve, which is bell-shaped and symmetric about the mean (µ = 0). It shows an area under the curve corresponding to the Z value we need to find. The shaded area under the curve to the left of a vertical line is labeled with the value 0.5999. This represents the cumulative area from the far left tail to the Z value. **Steps to Solve:** 1. **Graphical Representation:** - Identify the shaded area, which indicates the cumulative probability (area to the left of the Z value). 2. **Using a Graphing Calculator:** - To find the Z value corresponding to the cumulative area of 0.5999, use the inverse normal distribution function on the calculator. - Input 0.5999 as the cumulative probability to retrieve the corresponding Z value. 3. **Round to Four Decimal Places:** - Once the Z value is found, round it to four decimal places for precision. **Student Practice:** **Example Calculation:** - Given cumulative area: 0.5999 - Using a graphing calculator or Z-table, find the corresponding Z value. - The process will yield an approximate Z value, which students should then round to four decimal places. **Answer Submission:** - Students will input their Z value into the provided field and submit their answers for evaluation. **Conclusion:** Understanding how to calculate Z values from given areas is crucial in statistics for interpreting probabilities and making data-driven decisions. Practice with various cumulative areas to become proficient at using normal distribution curves and Z-scores. © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center
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