he physical plant at the main campus of a large state university receives daily requests to replace florescent light-bulbs. The distribution of the number of daily requests is Normally distributed with a mean of 47 and a standard deviation of 10. Using the Empirical Rule, what is the approximate percentage of light-bulb replacement requests numbering between 47 and 57?

47.75 %

Step-by-step explanation:

It is a very well known issue that in Standard Normal Distribution porcentages of all values fall according to:

μ + σ will contain a 68.3 %

μ + 2σ will contain a 95.5 %

μ + 3σ will contain a 99.7 %

However it is extremely importan to understand that the quantities above mentioned are distributed simmetrically at both sides of the mean, that is, the intervals are:

[ μ - 0,5σ; μ + 0,5σ ]

[ μ - 1σ; μ + 1σ ]

[ μ - 1.5σ; μ + 1.5σ ]

So we have to take that fact into account when applying the empirical rule. Then

With mean μ = 47 and σ = 10 is equal to say

values between 47 and 57 (μ + σ) we are talking about the second interval, but just half of it.

Then the approximate porcentage of light-bulb replacement requests is

95.5 / 2 = 47.75 %