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 µ = 400 and σ= 60. Suppose the manager takes a random sample of 45 employees and calculates the mean score, x. A) What is the shape of the sampling distribution of x for sample os size n = 45 from this population? Justify.
B) For the random sample taken by the manager, the mean score was 425. He is concerned the machinists may have cheated on the test. Calculate the probability that the mean score is 425 or greater. Make sure to show all calculations.
C) Does the manager have convincing evidence that the machinists cheated? Explain.