Most binomial probability calculations required in these exercises can be done by using Table C or the Normal approximation. Your instructor may request that you use the binomial probability formula or software. In exercises requiring the Normal approximation, you should use the continuity correction if you studied that topic.

Question 5.25

5.25 Getting to work.

Many U.S. cities are investing and encouraging a shift of commuters toward the use of public transportation or other modes of non-auto commuting. Among the 10 largest U.S. cities, New York City and Philadelphia have the two highest percentages of non-auto commuters at 73% and 41%, respectively.8

  1. If you choose 10 NYC commuters at random, what is the probability that more than half (that is, six or more) are non-auto commuters?
  2. If you choose 100 NYC commuters at random, what is the probability that more than half (that is, 51 or more) are non-auto commuters?
  3. Repeat part (a) for Philadelphia.
  4. Repeat part (b) for Philadelphia.

5.25

(a) 0.8963. (b) > 0.9998 or almost 1. (c) 0.1834. (d) 0.0212.