Suppose that a basketball player named Jose makes 60% of his free throws, and Kayla makes 70% of her free throws. Each player attempts 100 free throws at the end of practice one day. Regard these as independent random samples for each player. They plan to calculate the difference in their sample proportions of successfully made free throws, p(vector)_Kayla − p(vector)_Jose. 

a. Explain what the event (p(vector)_Kayla − p(vector)_Jose > 0) means in this context. 

b. Is it reasonable to approximate the sampling distribution of (p(vector)_Kayla − p(vector)_Jose) with a normal distribution? Explain why or why not. 

c. Determine the mean and standard deviation of (p(vector)_Kayla − p(vector)_Jose). 

d. Calculate the z-score corresponding to (p(vector)_Kayla − p(vector)_Jose = 0). e. Use the z-score to approximate the probability that (p(vector)_Kayla − p(vector)_Jose > 0).