II. PROBLEM SOLVING. Solve the following problems. SHOW YOUR COMPLETE SOLUTION 1. A tire manufacturer claims that its tires have a mean life of 40,000 kms. A random sample of 46 of these tires is tested and the sample mean is 38,000 kms. Assume that the populations standard deviation is 2,000 kms and the lives of tires are approximately normally distributed. a. . What test statistic should be used? b. What is the computed value at 5% level of significance? 2. The manager of a certain TV station claimed that the average rating of people watching their noontime teleserye in Manila is 62.5. A researcher randomly selected 25 people and asked them their favorite noontime teleserye. He computed the mean and obtained 67.8 with standard deviation of 15.9. Is there a reason to believe that the manager is correct? Use 0.01 as the level of significance.II. PROBLEM SOLVING. READ the problem and answer the following questions. 1. In the recent city triathlon, the sponsors have encouraged more women to participate in the event. A sample is chosen randomly and among 70 runners, 32 are women. The sponsors would somewhat like to be 90% certain that at least 40% of the participants are women. A. What test statistic should be applied in the problem? B. What is the value of p? (SHOW YOUR COMPLETE SOLUTION) C. What is the value of the test statistic? (SHOW YOUR COMPLETE SOLUTION)