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Q19. Labor trends were recently studied using a survey of respondents who were either unemployed (A) or employed (B). The survey results revealed that among those surveyed, 70% of those currently unemployed gain employment within the following month, and 30% remain unemployed. Meanwhile, 80% of those currently employed maintain employment through the following month, and 20% become unemployed. Suppose 75% of the population is currently employed. 0.3 A 0.7 0₂ B 0.8 0.2 Using the probabilities and states given, what percentage of the population will likely be employed two months from now? (Enter numerical value only. Do not enter % sign. Round the percentage to 1 decimal place, or to the nearest tenth of a percent.) (Ctrl)

Q19. Labor trends were recently studied using a survey of respondents who were either unemployed (A) or employed (B). The survey results revealed that among those surveyed, 70% of those currently unemployed gain employment within the following month, and 30% remain unemployed. Meanwhile, 80% of those currently employed maintain employment through the following month, and 20% become unemployed. Suppose 75% of the population is currently employed. 0.3 A 0.7 0₂ B 0.8 0.2 Using the probabilities and states given, what percentage of the population will likely be employed two months from now? (Enter numerical value only. Do not enter % sign. Round the percentage to 1 decimal place, or to the nearest tenth of a percent.) (Ctrl)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 23PPS
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**Labor Trends Study: Employment and Unemployment Transitions** **Background** Recent labor trends were analyzed based on survey data, classifying respondents as either unemployed (State A) or employed (State B). The survey revealed key insights into employment transitions over time: - **Currently Unemployed (State A)**: 70% transition to employment within the following month; 30% remain unemployed. - **Currently Employed (State B)**: 80% maintain their employment status the following month; 20% become unemployed. **Current Employment Statistics** - 75% of the population is currently employed. **Transition Diagram Explanation** - **State A (Unemployed) to State B (Employed)**: There is a transition probability of 0.7 (or 70%) from unemployment to employment. - **State B (Employed) to State A (Unemployed)**: A reverse transition probability of 0.2 (or 20%) indicates employed individuals becoming unemployed. - **State A to State A**: A self-loop with a probability of 0.3 (or 30%) shows the likelihood of remaining unemployed. - **State B to State B**: A self-loop with a probability of 0.8 (or 80%) indicates continuation in employment. **Problem Statement** Using the given probabilities and states, calculate the percentage of the population predicted to be employed two months from now. Provide the numerical value, rounded to one decimal place or the nearest tenth of a percent, without using the percentage sign.
Transcribed Image Text:**Labor Trends Study: Employment and Unemployment Transitions** **Background** Recent labor trends were analyzed based on survey data, classifying respondents as either unemployed (State A) or employed (State B). The survey revealed key insights into employment transitions over time: - **Currently Unemployed (State A)**: 70% transition to employment within the following month; 30% remain unemployed. - **Currently Employed (State B)**: 80% maintain their employment status the following month; 20% become unemployed. **Current Employment Statistics** - 75% of the population is currently employed. **Transition Diagram Explanation** - **State A (Unemployed) to State B (Employed)**: There is a transition probability of 0.7 (or 70%) from unemployment to employment. - **State B (Employed) to State A (Unemployed)**: A reverse transition probability of 0.2 (or 20%) indicates employed individuals becoming unemployed. - **State A to State A**: A self-loop with a probability of 0.3 (or 30%) shows the likelihood of remaining unemployed. - **State B to State B**: A self-loop with a probability of 0.8 (or 80%) indicates continuation in employment. **Problem Statement** Using the given probabilities and states, calculate the percentage of the population predicted to be employed two months from now. Provide the numerical value, rounded to one decimal place or the nearest tenth of a percent, without using the percentage sign.
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