An essential tool in the monitoring of the quality of a manufactured product is acceptance sampling. An acceptance sampling plan involves knowing the distribution of the life length of the item produced and determining how many items to inspect from the manufacturing process. The Journal of Applied Statistics (Apr. 2010) demonstrated the use of the exponential distribution as a model for the life length x of an item (e.g., a bullet). The article also discussed the importance of using the median of the lifetime distribution as a measure of product quality, since half of the items in a manufactured lot will have life lengths exceeding the median. For an exponential distribution with mean u, give an expression for the median of the distribution.
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