1. Measuing blood pressure is a vital process in determining a patient's immediate health condition. If the systolic blood pressure exceeds 150mm Hg, the patient is considered to
have high blood pressure and medication may be prescribed. Assume that a patient's
systolic blood pressure reading during a given day follows a normal distribution with a
mean of 160mm Hg and a standard deviation of 20mm Hg.
(a) If 5 readings are taken at various times during the day, determine the probability that
the average blood pressure reading will be less than 150mm Hg and hence, fail to
indicate that the patient has a high blood pressure problem
(6) Determine the number of readings required so that the probability is at most 1% of
failing to detect that a patient has high blood pressure.
(20 marks)