The reliability of a widely used microprocessor is typically expressed as time between failures (TBF). Suppose TBF is an exponentially distributed random variable that averages 3,000 cycles with a standard deviation of 54.776 cycles.
Suppose the purchaser of these microprocessors will draw a random sample of size 36, calculate a sample mean and standard deviation and then reject the shipment if the sample average falls below some agree-upon value. What value would ensure that approximately 97.5% of all shipments are accepted?