In a poll conducted by a survey firm, 82% of respondents said that their jobs were sometimes or always stressful. Eleven workers are chosen at random. What is the probability that more than 9 of Them find their jobs stressful?
A) 0.3164
B) 0.3849
C) 0.6836
D) 0.6151

Question

Quizplus · Accepted Answer

The probability that more than 9 out of 11 workers find their jobs stressful can be calculated using the binomial probability formula. Since the probability of a single worker finding their job stressful is 0.82, we need to find the probability of exactly 10 and exactly 11 workers finding their jobs stressful, and then sum these probabilities.For exactly 10 workers: $P(X=10) = \binom{11}{10}(0.82)^{10}(0.18)^{1}$For exactly 11 workers: $P(X=11) = \binom{11}{11}(0.82)^{11}(0.18)^{0}$Summing these probabilities gives the total probability of more than 9 out of 11 workers finding their jobs stressful, which is approximately 0.3849.

In a Poll Conducted by a Survey Firm, 82% of Respondents