Suppose that a tire manufacturer believes that the lifetimes of its tires follow a normal distribution with mean 50,000 miles and standard deviation 5,000 miles.
1. Based on the empirical rule, about 95% of tires last for between what two values for miles?
2. How many standard deviations above the mean is a tire that lasts for 58,500 miles? Record your answer with two decimal places of accuracy. I
3. Determine the percentage of tires that last for more than 58,500 miles. Record your answer as a percentage with two decimal places of accuracy, but do not include the % symbol. (Here and below, you may use Table Z or the Normal Probability Calculator applet or Excel or another software tool.)
4. Determine the mileage for which only 25% of all tires last longer than that mileage. Record your answer to the nearest integer value.
5. Suppose the manufacturer wants to issue a money back guarantee for its tires that fail to achieve a certain number of miles. If they want 99% of the tires to last for longer than the guaranteed number of miles, how many miles should they guarantee? Record your answer to the nearest integer value.
