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 5.35

5.35 Checking for survey errors.

One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 13% of American adults are black. The number of blacks in a random sample of 1500 adults should, therefore, vary with the binomial distribution.

  1. What are the mean and standard deviation of ?
  2. Use the Normal approximation to find the probability that the sample will contain 170 or fewer black adults. Be sure to check that you can safely use the approximation.

5.35

(a) . (b) 0.0274.