A synthetic fiber used in manufacturing carpet has tensile that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. (a) Find the probability that a random sample of n = 6 fiber specimens will have a sample mean tensile strength that exceeds 75.75 psi. 75.75 - р X- р M P[X > 75.75] = P o In o Tn 75.75 – 75.5 P[X > 75.75] = P2> 3.5 va = P[Z > 0.175] = 1-0(0.175) = 0.4325 BC (b) How is the standard deviation of the sample mean changed when the sample size is increased from n = 6 to n = 49?