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
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
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.
To find the range where approximately the middle 95% of the distribution falls, we can use the concept of the standard deviation.
In a normal distribution, approximately 95% of the data falls within two standard deviations from the mean.
Given that the mean is 75 jobs per day and the standard deviation is 10, we can calculate the range as follows:
Lower limit = mean - (2 * standard deviation)
Upper limit = mean + (2 * standard deviation)
Lower limit = 75 - (2 * 10) = 75 - 20 = 55 jobs per day
Upper limit = 75 + (2 * 10) = 75 + 20 = 95 jobs per day
Therefore, we can expect that most (approximately the middle 95%) of the distribution falls between 55 and 95 jobs per day.
The answer is option C: between 55 and 95 jobs per day.