Question

workers (in millions) by occupation for the u.s. natural resources, construction, maintenance 13.4 production, transportation, material moving 18.2 sales, office 29.7 service 22.9 management, professional 63.6 figure for exercises 83–86 using a pie chart to find probabilities in exercises 83–86, use the pie chart at the left, which shows the number of workers (in millions) by occupation for the united states. (source: u.s. bureau of labor statistics) 83. find the probability that a worker chosen at random is employed in a natural resources, construction, or maintenance occupation. 84. find the probability that a worker chosen at random is not employed in a service occupation. 85. find the probability that a worker chosen at random is employed in a sales or office occupation. 86. find the probability that a worker chosen at random is not employed in a production, transportation, or material moving occupation.

Explanation:

Step1: Calculate total workers

Sum all occupation values: $13.4 + 18.2 + 63.6 + 21.9 + 29.7 = 146.8$ million

Step2: Find target workers for 83

Natural resources, construction, maintenance: $13.4$ million
Probability: $\frac{13.4}{146.8} \approx 0.0913$

Step3: Find service workers for 84

Service workers: $21.9$ million
Probability not service: $1 - \frac{21.9}{146.8} \approx 1 - 0.1492 = 0.8508$

Step4: Find sales/office workers for 85

Sales, office workers: $29.7$ million
Probability: $\frac{29.7}{146.8} \approx 0.2023$

Step5: Find production workers for 86

Production workers: $18.2$ million
Probability not production: $1 - \frac{18.2}{146.8} \approx 1 - 0.1240 = 0.8760$

Answer:

1. Approximately 0.091
2. Approximately 0.851
3. Approximately 0.202
4. Approximately 0.876

(Note: Exact fractions can also be used, e.g., 83: $\frac{67}{734}$)