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Answer :
The standard deviation of the possible outcomes is approximately 15.24 hours.
To calculate the standard deviation of the possible outcomes, we first need to find the mean or expected value of the work hours. We can do this by multiplying each work hour by its corresponding probability, and then summing up the results:
Expected value = (0.3 x 45) + (0.2 x 40) + (0.4 x 25) + (0.1 x 12) = 30.3
Next, we need to find the variance of the possible outcomes. The variance is the average of the squared deviations of each outcome from the expected value. We can calculate the variance using the formula:
Variance = (sum of (x - mean)^2 * probability)
where x is the work hours and the sum is taken over all possible outcomes.
Variance = (0.3 x (45 - 30.3)^2) + (0.2 x (40 - 30.3)^2) + (0.4 x (25 - 30.3)^2) + (0.1 x (12 - 30.3)^2) = 231.87
Finally, we can calculate the standard deviation as the square root of the variance:
Standard deviation = sqrt(231.87) = 15.24
Learn more about standard deviation at: brainly.com/question/23907081
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