For a certain hockey team, the offensive players have made 75% of their attempted penalty shots and the defensive players have made 68% of their attempted penalty shots. The coach selects players at random to shoot penalty shots during practice and records the proportion of made penalty shots. At the end of practice, the offensive players have shot 53 penalty shots and the defensive players have shot 61 penalty shots. Let p, and p, be the sample proportions of made penalty shots by offensive and defensive players, respectively. a) What is the shape of the sampling distribution of P – P2 ? Why?
b) Find the mean and standard deviation of the sampling distribution.
Mean:
Standard Deviation: