The average lifetime of certain type of vehicle is 10 years with a standard deviation of 2 years. To spur on sales, the manufacturer wants to offer a warranty that will cover all repair or replacement costs on new vehicles for a period of time. If the manufacturer is willing to pay these costs for at most 3% of the cars that fail, for how long should a warranty provide coverage (in years)? Assume the lifetime of a car follows a normal distribution.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.