Question: One-third of all patients who undergo a non-invasive but unpleasant medical test require a sedative. A laboratory performs 20 such tests daily. Let X denote the number of patients on any given day who require a sedative.

a. Verify that X satisfies the conditions for a binomial random variable, and find n and p.

b. Find the probability that on any given day between five and nine patients will require a sedative (include five and nine).

c. Find the average number of patients each day who require a sedative.

d. Using the cumulative probability distribution for X in Chapter 12 "Appendix", find the minimum number x min of doses of the sedative that should be on hand at the start of the day so that there is a 99% chance that the laboratory will not run out.