A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately bell​ shaped, with a mean of 75

Question

jobs and a standard deviation of 10
.
Where would one expect most​ (approximately the middle​ 95%) of the distribution to​ fall?

A.
between 65

and 85

jobs per day
B.
between 55

and 105

jobs per day
C.
between 55

and 95

jobs per day
D.
between 45

and 105

jobs per day

Answer 1

To find where approximately the middle 95% of the distribution falls, we need to find the range that includes 95% of the data.

Using the empirical rule (also known as the 68-95-99.7 rule), we know that in a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

In this case, the mean is 75 jobs per day, and the standard deviation is 10 jobs per day.

Two standard deviations above and below the mean would be:

Mean - 2(Standard Deviation) = 75 - 2(10) = 75 - 20 = 55 jobs per day
Mean + 2(Standard Deviation) = 75 + 2(10) = 75 + 20 = 95 jobs per day

Therefore, we would expect most (approximately the middle 95%) of the distribution to fall between 55 and 95 jobs per day.

Therefore, the answer is C. between 55 and 95 jobs per day.