A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 86 jobs and a standard deviation of 12. Where do we expect approximately 95% of the distribution to fall?Group of answer choicesbetween 62 and 110 jobs per daybetween 50 and 122 jobs per daybetween 110 and 122 jobs per daybetween 74 and 98 jobs per day
Question
A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 86 jobs and a standard deviation of 12. Where do we expect approximately 95% of the distribution to fall?Group of answer choicesbetween 62 and 110 jobs per daybetween 50 and 122 jobs per daybetween 110 and 122 jobs per daybetween 74 and 98 jobs per day
Solution
The 95% of a distribution in a mound-shaped and symmetric (normal) distribution falls within approximately 2 standard deviations of the mean.
Given that the mean (μ) is 86 jobs and the standard deviation (σ) is 12 jobs, we can calculate the range as follows:
Lower limit = μ - 2σ = 86 - 2(12) = 62 Upper limit = μ + 2σ = 86 + 2(12) = 110
So, we expect approximately 95% of the distribution to fall between 62 and 110 jobs per day.
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