1. Given that the probability of a patient aged 30-45 not surviving to 1 year after replacement of two heart valves 0.12 and assuming that a doctor performs 50 such surgeries in a year, find the following probabilities a) Probability that exactly 8 patients will not survive the year. b) Probability that 48 or more of the patients will survive the first year. c) Probability that less than 3 of the patients will not survive the first year. 2. In a pilot study the distribution of fasting plasma cholesterol and triglyceride levels of a population of 3-month survivors of myocardial infarction was found to be normally distributed with a mean of 181 and a standard deviation of 15 mg/100 ml. Assuming these can be applied to the population of 3-month myocardial infarction survivors find the probability that a random such person would have a) a cholesterol level of more than 205 mg/100 ml. b) a cholesterol level of between 172 and 198 mg/100 ml. Also find c) the cholesterol level above which the top 10% of the population lie. d) the cholesterol levels which bracket the middle 50% of the cholesterol values