Find the Probability for the given problem under Normal distribution.
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Suppose that the number of milligrams of prophyrin per deciliter of blood is approximately normally distributed with mean 38 and standard deviation 12.
a) Status the random variable.
b) What is the probability that the number of milligrams of prophyrin per deciliter of blood is less than 60?
c) What is the probability that the number of milligrams of prophyrin per deciliter of blood is greater than 16?
d) What is the probability that the number of milligrams of prophyrin per deciliter of blood is between 40 and 60?
e) A person who may have an infection, anemia, or other type of illness, has a prophyrin level in the greater than 3.5 percent of the population. If a person has more than 65 milligrams of prophyrin per deciliter of blood, might they have an illness? Describe by finding the probability that the number of milligrams of prophyrin per deciliter of blood is more than 65.