On World Hepatitis Day, July 28, 2014, the BC Centre for Disease Control stated that 3% of British Columbians (about 130,000 people) were infected with hepatitis C. Although there is no vaccination against hepatitis C, it can be cured with a daily combination pill that cures 95% of patients.

a) In a survey of 2500 randomly selected British Columbians, what is the expected number that have hepatitis C? What is the probability that the proportion in the sample with hepatitis C is less than 2%?

b) Suppose the average age of people in the survey is 45.2 years and the standard deviation is 12.5 years. Calculate the standard error of the average age.

c) Suppose 80 people in your sample have hepatitis C. What is the probability that they can all be cured using the daily combination pill?

d) If it is not possible to answer any of the above questions in (a) to (c) because the sample size is too small, how large would the sample size need to be in order to answer the question?