2. A researcher wants to estimate the average time it takes to recover from "summeritis" after using the drug "sheeceeceeeshicillin". Assume that the times are normally distributed with a standard deviation of 3 days. How large a sample must she take to obtain a 99% confidence interval and be accurate within 1 day? (4 marks) 3. The probability of a flight from Toronto to Vancouver arriving on time is 88%. A random sample of 400 flights is examined. Show that a normal approximation is reasonable, then use the normal approximation to determine the probability that 370 flights or more arrive on time. [4 marks] 4. Mr. Li devises a new slingshot that he wants to market to students for pulling graduation pranks. During his testing, he finds that it has a mean firing distance of 50.6 metres with a standard deviation of 7.8 metres. He does 50 firing tests. Find a 90% confidence interval for the actual mean firing distance of the slingshot. What distance should Mr. Li use to truthfully advertise for his slingshot? [4 marks]