The depth from the surface of Earth to a refracting layer beneath the surface can be estimated using methods developed by seismologists. One method is based on the time required for vibrations to travel from a distant explosion to a receiving point. The depth measurement (M) is the sum of the true depth (D) and the random measurement error (E). That is, M=D+E. The measurement error (E) is assumed to be normally distributed with mean 0 and standard deviation 1.5 feet. 1. If the true depth at a certain point is 2 feet, what is the probability that the depth measurement will be negative?
2. Suppose three independent depth measurements are taken at a point where the true depth is 2 feet. What is the probability that at least one of these measurements will be negative?
3. What is the probability that the mean of the three independent depth measurements taken at the point where the true depth is 2 feet will be negative?