Playing 10 rounds of golf on his home course, a golf professional averaged 71.3 with a standard deviation of 2.64 .

(a) Test the null hypothesis that the consistency of his game on his home course is actually measured by \(\sigma=2.40\), against the alternative hypothesis that he is less consistent. Use the level of significance 0.05 . Assume that the distribution of his score, although discrete, is approximately normal.

(b) If the distribution of his scores has a long righthand tail, are your calculations in part (a) valid? Explain.