A manufacturing company has designed a new test of mechanical aptitude.All of the machinists were required to take the test.The distribution of the scores is moderately skewed right with = 425 and =65.Suppose the manager takes a random sample of 40 employees and calculate the mean score.

A.What is the shape of the sampling distribution offor samples of size n = 40 from this population?Justify

B.For the random sample taken by the manager, the mean score was 450.He is concerned the machinists may have cheated on the test.Calculate the probability that the mean score is 450 or greater.

C.Does the manager have convincing evidence that the machinists cheated?Explain.