Question

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). Use “Continuity correction factor” method. Use Table 1 in Appendix B.

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 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?

Explain.

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Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,500 and $14,600.

1. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
2. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
3. What amount should you bid to maximize the probability that you get the property (in dollars)?
   
   
4. Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,250. If your objective is to maximize the expected profit, what is your bid?

What is the expected profit for this bid (in dollars)?

Answer 1