Question 2. A consumer wishes to estimate the proportion of processed food items that contain genetically modified {GM} products. {a} If no preliminary study is available, how large a sample size is needed to be 99 percent confident the estimate is within 0.03 of p? {b} In a preliminary study, 210 of 350 processed items contained GM products. Using this preliminary study, how large a sample size is needed to construct a 99% condence interval within 0.03 of p? Question 3. Suppose that the insurance companies did do a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up. {a} Construct a 75% confidence interval for the population proportion who claim they always buckle up and write the interpretation (Sketch the graph}. {b} Which distribution you used for this problem? Explain your choice. Question 4. The standard deviation of the weights of elephants is known to be approximately 15 pounds. If we want to be 99% condent that the sample mean weight is within three pounds of the true population mean weight of elephants, how many randomly selected elephants must be chosen for the sample