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Binomial Distributions, Geometric Distributions, and Sampling Distributions Cumulative Review Problems

By — McGraw-Hill Professional
Updated on Feb 4, 2011

Review the following concepts if necessary:

Problems

  1. An unbalanced coin has p = 0.6 of turning up heads. Toss the coin three times and let X be the count of heads among the three coins. Construct the probability distribution for this experiment.
  2. You are doing a survey for your school newspaper and want to select a sample of 25 seniors. You decide to do this by randomly selecting 5 students from each of the 5 senior-level classes, each of which contains 28 students. The school data clerk assures you that students have been randomly assigned, by computer, to each of the 5 classes. Is this sample
    1. a random sample?
    2. a simple random sample?
  3. Data are collected in an experiment to measure a person's reaction time (in seconds) as a function of the number of milligrams of a new drug. The least squares regression line (LSRL) for the data is Reaction Time = 0.2 + 0.8(mg). Interpret the slope of the regression line in the context of the situation.
  4. If P(A) = 0.5, P(B) = 0.3, and P(A or B) = 0.65, are events A and B independent?
  5. Which of the following is (are) examples of quantitative data and which is (are) examples of qualitative data?
    1. The height of an individual, measured in inches.
    2. The color of the shirts in my closet.
    3. The outcome of a flip of a coin described as "heads" or "tails."
    4. The value of the change in your pocket.
    5. Individuals, after they are weighed, are identified as thin, normal, or heavy.
    6. Your pulse rate.
    7. Your religion.

Solutions

  1. The sample space for this event is {HHH, HHT, HHT, HHT, HTT, HTH, THH, TTT}. One way to do this problem, using techniques developed in Chapter 9, is to compute the probability of each event. Let X = the count of heads. Then, for example (bold faced in the list above), P(X = 2) = (0.6)(0.6)(0.4) + (0.6)(0.4)(0.6) + (0.4)(0.6)(0.6) = 3(0.6)2(0.4) = 0.432. Another way is to take advantage of the techniques developed in this chapter (noting that the possible values of X are 0, 1, 2, and 3):
  2. Be sure to check that the sum of the probabilities is 1 (it is!).

  3.  
    1. Yes, it is a random sample because each student in any of the 5 classes is equally likely to be included in the sample.
    2. No, it is not a simple random sample (SRS) because not all samples of size 25 are equally likely. For example, in an SRS, one possible sample is having all 25 come from the same class. Because we only take 5 from each class, this isn't possible.
  4. The slope of the regression line is 0.8. For each additional milligram of the drug, reaction time is predicted to increase by 0.8 seconds. Or you could say for each additional milligram of the drug, reaction time will increase by 0.8 seconds, on average.
  5. P(A or B) =P(AB) = P(A) + P(B) – P(AB) = 0.5 + 0.3 – P(AB) = 0.65 P(AB) = 0.15. Now, A and B are independent if P(AB) = P(A)·P(B). So, P(A)·P(B) = (0.3)(0.5) = 0.15 = P(AB). Hence, A and B are independent.
  6.  
    1. Quantitative
    2. Qualitative
    3. Qualitative
    4. Quantitative
    5. Qualitative
    6. Quantitative
    7. Qualitative

Review the following concepts if necessary:

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