1. suppose we collect the impact strength of a sample of five pieces of steel. their strengths are (in ft-lb units): 50, 48, 62, 53, 49. (a) calculate the sample mean and sample variance of the measurements. (b) suppose a new process has been created which results in the impact strength of the materials to change by the function, y = 3x + 1, that is, the new strength is more than three times its previous strength. noting that if y = ax + b, then y¯ = ax¯ + b and s 2 y = a 2 s 2 x , find the sample mean and sample variance of the new material.