Final answer:
The question is seeking the length of a warranty for dishwashers based on an exponential distribution, but the necessary information to solve this problem is not provided, such as the mean lifetime of the dishwashers or the failure rate.
Step-by-step explanation:
The question pertains to determining the warranty period for dishwashers such that only 10% would need to be replaced before the warranty expires. This is a statistical problem that involves using the exponential distribution to find out the time by which only a certain percentage of the product is expected to fail. Given that this is related to mean lifetimes and failure rates, one would typically use the cumulative distribution function (CDF) of the exponential distribution to solve for the time that corresponds to the 10% failure rate.
However, without the mean lifetime of the dishwashers or another piece of information like the rate parameter, we cannot determine the exact length of the warranty. The information provided in the references is about computer parts, phones, light bulbs, and CD players, but does not directly provide the information necessary to solve the question about dishwashers.