1. Your company makes a special light bulb that is supposed to have a long life. From previous tests you know that the lifetime of the bulb is normally distributed with a standard deviation of 40 hours. You take a random sample of 30 bulbs and calculate that the mean life is 780 hours. What is the 96% confidence interval for the population mean for all the light bulbs?
2. In the above problem, suppose that we wanted to be 96% confident that our sample mean was within 10 hours of the true mean. How big of a sample would we need?
3. You take a sample of 10 candy bars and use this to calculate the mean to be 230 calories and a standard deviation to be 15 calories. What is the 99% confidence interval for the true mean calorie count for these candy bars?