. The plastic tubes produced by company X for the irrigation system used in golf courses have a length of 1.5 meters and a standard deviation of 0.1 meter. The plastic tubes produced by company Y have a length of 1 meter and a standard deviation of 0.09 meter. Suppose that both tube lengths follow normal distributions. (a) Calculate the probability that a random sample of 15 tubes from company X has a mean length at least 0.45 meter greater than the mean length of a random sample of size 20 from company YI