Question 5 [13 marks] Hayley has recently purchased a blood pressure monitor. Suppose Hayley's blood pressure reading [in mmHg] on any given day, is normally distributed with unknown mean ii and variance 0-2 = 3135. Assume that these readings are independent from day to day. Hayley records her blood pressure everyday and randomly selects 50 of her previous blood pressure readings. 01 these readings. Hayley calculated the sum of all the readings to be 6118.16 and that 32 of them were less than 124.74. A. [3 marks] Using the sample data, test whether the true proportion o1 Hayley's blood pressure readings that are less than 124.74 is less than 05?. Clearly state your hypotheses and use a signicance level Ufa = 5%. B. [3 marks] Using the sample data, test whether it is equal to 122. Clearly state your hypotheses and use a signicance level o'i a = 5%. C. [4 marks] Calculate the probability of making a type II error for the test in part B at a significance level of a = 5%. if the true value of]! is 121.3. D. [3 marks] Hayley decides eating vegetables might be good for her blood pressure. On any day on which her blood pressure is below the 67th percentile. the number of vegetables Hayley eats. 'irom among a choice of 5 carrots, will be a binomial random variable with success probability 0.41. On any day on which her blood pressure is above the 67th percentile, the number of vegetables Hayley eats, from among a choice of 'i' radishes, will be a binomial random variable with success probability 0.72. Find the probability that Hayley eats 3 vegetables today. END OF EXAMINATION