Question

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.†

(a) For a sample of 14 Americans, what is the probability that at least 11 believe global warming is occurring? Use the binomial distribution probability function discussed in Section 5.5 to answer this question. (Round your answer to four decimal places.)

(b) For a sample of 140 Americans, what is the probability that at least 90 believe global warming is occurring? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(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?

A. As the number of trials becomes large, the normal approximation simplifies the calculations required to obtain the desired probability.

B. As the number of trials becomes large, the normal approximation gives a more accurate answer than the binomial probability function.

(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.

Answer 1

(a)

(b)

(c)

A. As the number of trials becomes large, the normal approximation simplifies the calculations required to obtain the desired probability.

(d)

the normal approximation of the binomial distribution discussed in Section 6.3, because the normal approximation simplifies the calculations required to obtain the desired probability.