Suppose that the expected number of accidents per week at an industrial plant is 5. Suppose also that the number of workers injured in each accident are independent random variables with a common mean of 2.5. If the number of workers injured in each accident is independent of the number of accidents that occur, what is the expected number of workers injured in a week?
Answers
Answer:
12.5
Step-by-step explanation:
If the number of workers injured in each accident is independent of the number of accidents that occur, then the expected number of workers injured in a week equals the expected number of accidents per week times the expected number of workers injured in each accident.
But the expected number of workers injured in each accident is precisely the average or mean, so
Expected number of workers injured in a week = 5*2.5 = 12.5.
Or in other words, in 10 weeks there will probably be 125 workers injured.
Final answer:
The expected number of workers injured in a week at the industrial plant is 12.5, calculated by multiplying the expected number of accidents per week (5) by the expected number of workers injured per accident (2.5).
Explanation:
The expected number of accidents at an industrial plant per week is given as 5 and the mean number of workers injured per accident is given as 2.5. As the number of workers injured per accident is stated to be independent from the number of accidents that occur, we can merely multiply the two expected values to find the overall expected value of workers injured in a week.
So, Expected number of workers injured per week = Expected number of accidents per week * Expected number of workers injured per accident = 5 * 2.5 = 12.5.
This implies that, on average, we can expect 12.5 workers to be injured at the industrial plant per week.
Learn more about Expectation of Random Variables here:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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2x² – 5x + 3 = m(x)
Answers
Answer:
- vertex: (1.25, -0.125)
- axis of symmetry: x = 1.25
- minimum: -0.125
- domain: all real numbers
- range: y ≥ -0.125
Step-by-step explanation:
For quadratic ax² +bx +c, the axis of symmetry is x = -b/(2a). For your function, a=2, b=-5, c=3 and the axis of symmetry is ...
x = -(-5)/(2(2)) = 5/4 = 1.25
The vertex is on the axis of symmetry. The y-value there is ...
m(5/4) = (2(5/4) -5)(5/4) +3 = (-5/2)(5/4) +3 = -25/8 +24/8 = -1/8
The vertex is (5/4, -1/8).
The axis of symmetry is x = 5/4.
The leading coefficient is positive, so the parabola opens upward. The vertex is a minimum.
The minimum is -1/8.
The function is defined for all values of x, so ...
the domain is all real numbers.
Values of y can only be -1/8 or greater, so ...
the range is y ≥ -1/8.