A survey of recent e-commerce start-up firms was undertaken at an industry convention. Representatives of the firm were asked for the geographic location of the firm as well as the firm's outlook for growth in the coming year. The results are provided below. Are the events “firm from the 2nd region” and “expects high growth” statistically independent?

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Any basketball fan knows that Shaquille O'Neal, one of the NBA's most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off- season, Shag had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. Check the conditions of the Central Limit Theorem for this scenario. Calculate the number of expected successes.