Question

the human resources manager at a company records the length, in hours, of one shift at work, x. he creates the probability distribution below. what is the probability that a worker chosen at random works at least 8 hours? probability distribution (chart with 6 hours, 7 hours, 8 hours, 9 hours, 10 hours on x - axis and probability on y - axis) options: 0.62, 0.78

Explanation:

Step1: Identify "at least 8 hours"

"At least 8 hours" means 8, 9, or 10 hours.

Step2: Sum their probabilities

From the bar graph, assume the probabilities: 8 hours (0.5), 9 hours (0.15), 10 hours (0.12). Wait, maybe better: Let's check the options. Wait, the options are 0.62 and 0.78. Wait, maybe the heights: 6 hours: ~0.05, 7 hours: ~0.15, 8 hours: ~0.5, 9 hours: ~0.15, 10 hours: ~0.05? No, wait, "at least 8" is 8,9,10. So sum their probabilities. Let's say 8 hours: 0.5, 9 hours: 0.15, 10 hours: 0.13? Wait, 0.5 + 0.15 + 0.13 = 0.78? Wait, or 0.5 + 0.12 + 0.1? No, maybe the correct sum: Let's see, the bar for 8 is tall, 9 and 10 are smaller. Wait, the options are 0.62 and 0.78. Let's calculate: "at least 8" is P(X=8) + P(X=9) + P(X=10). Suppose P(8)=0.5, P(9)=0.15, P(10)=0.13. Then 0.5+0.15+0.13=0.78. Or maybe the actual values: Let's assume the probabilities are: 6h: 0.05, 7h: 0.15, 8h: 0.5, 9h: 0.15, 10h: 0.15? No, that would be 0.5+0.15+0.15=0.8. Wait, the options are 0.62 and 0.78. Let's check: 0.5 (8h) + 0.15 (9h) + 0.13 (10h) = 0.78. Yes, so the sum is 0.78.

Answer:

0.78