Quandaries
and Queries 

Question: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function: f(x) = 8 for 11.975 ≤ x ≤12.10 a. What is the probability that a bottle will be filled with 12.02 or
more ounces? 

In my mind I see a graph of the density function.
Notice that the scales an the X and Y axes are not the same and there is a break in the Xaxis between 0 and 11.975. Notice also that the arera under the curve, that part shaded yellow, is 1 as it must be for a probability density function. I am going to do part b), and you can do parts a) and c). In b) you want the probability that x is between 12 and 12.05. On the diagram that is the area under the density function, between 12 and 12.05, the region shaded red in the diagram below.
This region is a rectangle so it area is the length times the width, that is
Thus the probability that a bottle will be filled between 12 and 12.05 ounces is 0.4 Cheers,


