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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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