Question

ol. Stress at work: In a poll conducted by the General Social Survey, 80% of respondents said that their jobs were sometimes or always stressful. One hundred and ninety workers are chosen at random. Use the TI-84 Plus calculator as needed. Round your answer to at least four decimal places. (a) Approximate the probability that 140 or fewer workers find their jobs stressful. (b) Approximate the probability that more than 155 workers find their jobs stressful. (c) Approximate the probability that the number of workers who find their jobs stressful is between 145 and 158 inclusive.

Answer 1

Let X be the number of respondents who find their job stressful.

So

X ~Bin( 190,0.8)

1)

$P(X \leq 140) = \sum_{i=0}^{140} \times (0.8)^i \times (0.2)^{190-i} = 0.0210$

2)

$P(X > 155) = \sum_{i=156}^{190} \times (0.8)^i \times (0.2)^{190-i} = 0.2664$

3)

$P(145 < X < 158) = \sum_{i=146}^{157} \times (0.8)^i \times (0.2)^{190-i} = 0.7204$

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