According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening (American Psychological Association website).

a. For a sample of 15 Americans, what is the probability that at least 12 believe global warming is occurring? Use the binomial distribution probability function discussed in Section 5.5 to answer this question.

b. For a sample of 150 Americans, what is the probability that at least 100 believe global warming is occurring? Use the normal approximation of the binomial distribution to answer this question.

c. As the number of trials in a binomial distribution application becomes large, what is the advantage of using the normal approximation of the binomial distribution to compute probabilities?

d. When the number of trials for a binomial distribution application becomes large, would developers of statistical software packages prefer to use the binomial distribution probability function shown in Section 5.5 or the normal approximation of the binomial distribution discussed in Section 6.3? Explain.