Refer to the Earthquake Engineering and Engineering Vibration (March 2013) study of the structural damage to a three-story building caused by seismic ground noise, Exercise 5.33. Recall that the acceleration Y (in meters per second-squared) of the seismic ground noise was modeled using a normal probability distribution. Assume  μ = .5 and unknown σ. Consider a random sample of n = 16 acceleration measurements from this population, and let Y̅ represent the sample mean and S the sample standard deviation.

a. Describe the sampling distribution of the statistic, T = 4(Y̅ - .5)/S.

b. Suppose the sample standard deviation is S = .015. Use this value, the result, part a, and statistical software to find the exact probability that the sample mean acceleration is less than .52 meters per sec².  

Data from Exercise 5.33

Seismic ground noise describes the persistent vibration of the ground due to surface waves generated from traffic, heavy machinery, winds, ocean waves, and earthquakes. A group of civil engineers investigated the structural damage to a three-story building caused by seismic ground noise in Earthquake Engineering and Engineering Vibration (March, 2013). The methodology involved modeling the acceleration Y (in meters per second-squared) of the seismic ground noise using a normal probability distribution.