Problem #1 (20 pts). A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample of n = 25 tubes of each type is selected, and X-X is computed. If H equals or exceeds A, the manufacturer would like to adopt type B for use. The observed difference is x-x=3.0. What is the probability that X, exceeds X, by 3.0 or more if g and are equal? Is there strong evidence that is greater than ^?