A company claims that the mean deflection of their 10-foot steel beams is 0.012 inches. A construction contractor who purchases large quantities of steel beams suspects that the manufacturer misleads its customers and that the true deflection is, in fact, larger than the one claimed. To see whether this suspicion is justified, the contractor selects n=10 beams at random from his inventory, determines their deflection as follows: 0.0132 0.0138 0.0108 0.0126 0.0136 0.0112 0.0124 0.0116 0.0127 0.0131 Conduct a full hypothesis testing to determine if the contractor's suspicion is valid at = 0.05. (10) 1ii In a survey poll of 500 adults, 205 prefer public transit in urban centers, 112 use their own vehicles, and 197 adults prefer other means of transportation (walking, biking, etc.). (4) a) Find the probability that an adult uses only the public transit OR their own vehicle in urban centers. (Draw a Venn diagram) (4) b) Find the probability that an adult uses both public transit AND their own vehicle in urban centers. (Draw a Venn diagram) (2) c) Are the two events mutually exclusive? Why or why not