Although we all experience inflammation associated with a bruise or sprain, inflammation can also affect the cells in the body. C-reactive protein (CRP) is a measure of inflammation and can be part of...

Although we all experience inflammation associated with a bruise or sprain, inflammation can also affect the cells in the body. C-reactive protein (CRP) is a measure of inflammation and can be part of a routine blood test. For healthy adults, the CRP level is less than 5 milligrams per liter of blood. Suppose the probability distribution for X, the CRP level in healthy adults, is given as follows:

a. Verify that this is a valid probability distribution.

b. What is the probability that a randomly selected healthy adult will have a CRP level less than 2.5?

c. What is the probability that a randomly selected healthy adult will have a CRP level between 2 and 3?

d. Find a value c such that 5% of healthy adults have a CRP level of at least c.

e. If a patient has a CRP level of at least 4, then additional testing is done. What is the probability that a healthy adult will need additional testing?

f. What is the probability that the fifth healthy adult will be the first to need additional testing?