In a study of hypertension and optimal treatment conducted by the National Heart Institute, 10,000 patients had a mean systolic blood pressure, # = 161 mm Hg and standard deviation, o = 25 mm Hg. Assume the systolic blood pressure is normally distributed. a) What is the probability of patients with a systolic blood pressure of more than 180 mm Hg? b) How many patients will have a systolic BP of more than 180 mm Hg? c) What is the probability of patients with a systolic blood pressure between 145 and 160 mmlg? d) If 60 random samples each of size 30 are drawn from this population, determine: i. the sampling distribution of the mean systolic blood pressure. ii. the probability that the of mean systolic blood pressure will be less than 165 mmlg