In a poll conducted by a survey firm, 75% of respondents said that their jobs were sometimes or always stressful. Nine workers are chosen at random. What is the probability that less than 4 of Them find their jobs stressful?
A) 0.0100
B) 0.9900
C) 0.0489
D) 0.0389

Question

Quizplus · Accepted Answer

The probability of a worker finding their job stressful is 0.75. The probability of a worker not finding their job stressful is 0.25. The probability of less than 4 workers finding their jobs stressful is the sum of the probabilities of 0, 1, 2, and 3 workers finding their jobs stressful. This can be calculated using the binomial distribution:P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)= (9 choose 0) * (0.75)^0 * (0.25)^9 + (9 choose 1) * (0.75)^1 * (0.25)^8 + (9 choose 2) * (0.75)^2 * (0.25)^7 + (9 choose 3) * (0.75)^3 * (0.25)^6= 0.0019 + 0.0146 + 0.0547 + 0.1367= 0.2079Therefore, the probability of less than 4 workers finding their jobs stressful is 0.2079, which is closest to choice A, 0.0100.

In a Poll Conducted by a Survey Firm, 75% of Respondents