A doctor diagnoses a patient as hypertensive and prescribes an antihypertensive medication. To assess the clinical status of the patient, the doctor takes n replicate blood-pressure measurements before the patient starts the drug (baseline) and n replicate blood-pressure measurements 4 weeks after starting the drug (follow-up). She uses the average of the n replicates at baseline minus the average of the nreplicates at follow-up to assess the clinical status of the patient. She knows, from previous clinical experience with the drug, that the mean diastolic blood pressure (DBP) change over a 4-week period over a large number of patients after starting the drug is 5.3 mm Hg with variance 32n, where n is the number of replicate measures obtained at both baseline and follow-up. (Assume that diastolic blood pressure can be measured exactly and no continuity correction is necessary.)

(a)If we assume the change in mean DBP is normally distributed, then what is the probability that a subject will decline by at least 5.3 mm Hg if 1 replicate measure is obtained at baseline and follow-up? (Round your answer to four decimal places.)

(b)The physician also knows that if a patient is untreated (or does not take the prescribed medication), then the mean DBP over 4 weeks will decline by 2.4 mm Hg with variance 32n. What is the probability that an untreated subject will decline by at least 5.3 mm Hg if 1 replicate measure is obtained at both baseline and follow-up? (Round your answer to four decimal places.)

(c)Suppose the physician is not sure whether the patient is actually taking the prescribed medication. She wants to take enough replicate measurements at baseline and follow-up so that the probability in part (a) is at least five times the probability in part (b). What is the smallest number of replicate measurements she can take? (Round your answer up to the next whole number.)