Problem: Common Last Names

The Census Bureau says that the 10 most common last names in the United States are (in order) Smith, Johnson, Williams, Jones, Brown, Davis, Miller, Wilson, Moore, and Taylor. These names account for 5.6% of all US residents. Consider our class as a random sample of 18 individuals.

a) Check if this situation fits the binomial setting.

b) Assuming it does, build the probability distribution as a table in StatCrunch. For your probability distribution table, since the probabilities will be very close to 0 after about X = 7, you may cut off the table after 7.

c) Find the probability that exactly 2 individuals have one of those last names. Provide a StatCrunch binomial graph displaying your answer.

d) Calculate the probability that at least one individual has one of those last names. Again, provide a StatCrunch binomial graph displaying your answer.

e) Calculate the probability that between 3 and 5 individuals (inclusive) have one of those last names. Use the probability distribution to answer this question (then verify it with a StatCrunch graph.

f) Find the mean and standard deviation of this probability distribution (you may use the binomial mean and standard deviation formulas in the notes).