Question

suppose the area that can be painted using a single can of spray paint is slightly variable and follows a nearly normal distribution with a mean of 25 square feet and a standard deviation of 3 square feet. suppose also that you buy three cans of spray paint. how much area would you expect to cover with these three cans of spray paint?

Answer 1

The expected area that can be covered by three cans of spray paint, each with a mean coverage of 25 square feet, is 75 square feet.

Step-by-step explanation:

The student has asked about the expected area that can be covered using three cans of spray paint where each can has a slightly variable area coverage that follows a nearly normal distribution. The mean coverage area of a single can is given as 25 square feet with a standard deviation of 3 square feet.

To calculate the expected total area covered by three cans, we simply multiply the mean area coverage of one can by the number of cans since the expectation is a linear operator.

Therefore, the expected area to be covered by three cans is 3 times 25 square feet, which equals 75 square feet.

It is important to note that we are considering the mean coverage for each can, and not adding standard deviations, since standard deviation does not sum linearly like means do.