A tire manufacturer produces tires that last 36,500 miles with a standard deviation of 5,000 miles.

1. Assuming these tires are normally distributed, what percentage of tires will last less than 37,800 miles?
2. Assuming these tires are normally distributed, how many tiresin a lot of 200 tires, would you expect to last less than 37,800 miles?
3. What is the percentage of tires between 35,000 and 37,000 miles?
4. If management wants to provide no more than 10% of the tires to be eligible for the discount guarantee, what should the guarantee mileage be?
5. How many miles a tire should last in order to be considered in the top 5% of durability?