In: Statistics and Probability
Stress at work: In a poll about work, 84% of respondents said that their jobs were sometimes or always stressful. Twelve workers are chosen at random. Round the answers to four decimal places.
(a) What is the probability that exactly 11 of them find their jobs stressful?
(b) What is the probability that more than 9 find their jobs stressful?
(c) What is the probability that fewer than 6 find their jobs stressful?
(d) Would it be unusual if fewer than 5 of them find their jobs stressful?
Use excel formula " =BINOM.DIST(x, n ,p, FALSE) "
=BINOM.DIST(x, 12, 0.84, FALSE) Where, x=0,1,2....12
x | Excel formula | P(X=x) |
0 | =BINOM.DIST(x, 12, 0.84, FALSE) | 0.0000 |
1 | =BINOM.DIST(1, 12, 0.84, FALSE) | 0.0000 |
2 | =BINOM.DIST(2, 12, 0.84, FALSE) | 0.0000 |
3 | =BINOM.DIST(3, 12, 0.84, FALSE) | 0.0000 |
4 | =BINOM.DIST(4, 12, 0.84, FALSE) | 0.0001 |
5 | =BINOM.DIST(5, 12, 0.84, FALSE) | 0.0009 |
6 | =BINOM.DIST(6, 12, 0.84, FALSE) | 0.0054 |
7 | =BINOM.DIST(7, 12, 0.84, FALSE) | 0.0245 |
8 | =BINOM.DIST(8, 12, 0.84, FALSE) | 0.0804 |
9 | =BINOM.DIST(9, 12, 0.84, FALSE) | 0.1876 |
10 | =BINOM.DIST(10, 12, 0.84, FALSE) | 0.2955 |
11 | =BINOM.DIST(11, 12, 0.84, FALSE) | 0.2821 |
12 | =BINOM.DIST(12, 12, 0.84, FALSE) | 0.1234 |
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It be unusual if fewer than 5 of then find their jobs stressful, since the probability is
Since the probability 0.0001 is less than 0.05. Therefore it is considered unusual.