Water permeability of concrete can be measured by letting water flow across the surface and determining the amount lost (in inches per hour). Suppose that the permeability index x for a randomly selected concrete specimen of a particular type is normally distributed with mean value 1000 and standard deviation 150.
a. How likely is it that a single randomly selected specimen will have a permeability index between 850 and 1300?
b. If the permeability index is to be determined for each specimen in a random sample of size 10, how likely is it that the sample mean permeability index will be between 950 and 1100? between 850 and 1300?