A CBS News/New York Times survey found that 97% of Americans believe that texting while driving should be outlawed (CBS News website, January 5, 2015).
a. For a sample of 10 Americans, what is the probability that at least 8 say that they believe texting while driving should be outlawed? Use the binomial distribution probability function to answer this question (to 4 decimals).
b. For a sample of 100 Americans, what is the probability that at least 95 say that they believe texting while driving should be outlawed? Use the normal approximation of the binomial distribution to answer this question. (to 4 decimals).
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?
Makes calculation of probabilities more precise
Avoids issues related to the Central Limit Theorem
Simplifies calculation of probabilities
Obviates the need of having independent events
d. When the number of trials for a binominal 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?
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