Question

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 62 jobs and a standard deviation of 12. Where do we expect most (approximately 95%) of the distribution to fall ?

Answer 1

The interval for a normal distribution (bell-shaped) where we expect approximately 95% of the distribution to fall is given by:

$(\mu-2\sigma,\mu+2\sigma)$

where μ is the mean and σ is the standard deviation of the distribution.

In this problem, we have:

$\begin{gathered} \mu=62 \\ \sigma=12 \end{gathered}$

Therefore, we expect approximately 95% of the distribution to fall in the interval:

$\begin{gathered} (62-2\cdot12,62+2\cdot12) \\ \\ (62+24,62-24) \\ \\ (38,86) \end{gathered}$

Thus, the answer is: from 38 to 86 jobs submitted per day.