Estimating sample size using military significant difference. suppose we are buying a new system that is designed to have an infrared detection range of 14.0 km or more. if the actual infrared detection range is less than 11.5 km, the effectiveness of the system would not support mission requirements. during testing we are willing to accept a probability of type 1 error (alpha) of 0.05, but we want to have a 0.975 probability of detecting a "bad" system. prior test results indicate that the standard deviation of the detection range is normally distributed and should be about 2.8 km. how many trials do you estimate will be required to meet this criteria?