The area under a normal curve with mu = 8 and sigma = 3 is
It's just rock and roll...
1 sigma does not represent 68.8 percent of anything.The area under the standard normal curve, between -0.5 and +0.5, that i, the central 1 sigma, is equal to 0.68269 or 68.3%.
What is the area under the normal curve between z equals 0.0 and z equals 2.0?
It is 0.
The area is 0.008894
By standard practice, the normal distribution curve should be normalized so that the area under the curve is 1. This results in a height, at the mean, of about 0.4, i.e. the probability of a sample value being equal to the mean is 40 percent. The width of the normal distribution curve is infinite, as the tails are asymptotic to the X axis. It is easier to understand that the +/- one sigma area is 68.2 percent, the +/- two sigma area is 95.4 percent, and the +/- three sigma area is 99.6 percent.