Homework SourseA metal cutting plant is concerned with accidents The table
A metal cutting plant is concerned with accidents. The table gives the distribution for the number of accidents per month:
A) find the probability that one or fewer accidents will occur.
B) find the probability that more than one but fewer than 5 accidents will occur.
c) find the expected number of accidents.
d) find the variance and standard deviation for the number of accidents
| y | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| p(y) | 0.716 | 0.180 | 0.060 | 0.020 | 0.010 | 0.010 | 0.002 | 0.000 | 0.002 |
Solution
a)
P(1 or fewer) = P(0) + P(1) = 0.716+0.180 = 0.896 [ANSWER]
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b)
P(more than 1 but fewer than 5) = P(2) + P(3) + P(4)
= 0.060 + 0.020 + 0.010
= 0.090 [ANSWER]
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c)
Consider:
Thus,
E(x) = Expected value = mean = 0.478 [ANSWER]
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D)
Var(x) = E(x^2) - E(x)^2 = 0.981516 [ANSWER, VARIANCE]
Thus,
s(x) = sqrt [Var(x)] = 0.990714893 [ANSWER, STANDARD DEVIATION]
| x | P(x) | x P(x) | x^2 P(x) |
| 0 | 0.716 | 0 | 0 |
| 1 | 0.18 | 0.18 | 0.18 |
| 2 | 0.06 | 0.12 | 0.24 |
| 3 | 0.02 | 0.06 | 0.18 |
| 4 | 0.01 | 0.04 | 0.16 |
| 5 | 0.01 | 0.05 | 0.25 |
| 6 | 0.002 | 0.012 | 0.072 |
| 7 | 0 | 0 | 0 |
| 8 | 0.002 | 0.016 | 0.128 |
