1. Using the information provided, describe, through graphical summaries and numerical summaries such as the mean and standard deviation, each probability distribution.

2. Does it appear that, on average, the Neuländers were successful in signing more than one family from a parish? Does it seem likely that most of the families knew one another prior to undertaking the voyage? Explain your answers for both questions.

3. Using the mean number of freights purchased per family, estimate the average cost of the crossing for a family in pistoles and in U.S. dollars.

4. Is it appropriate to estimate the average cost of the voyage from the mean family size? Why or why not?

5. Langenscheidt came across a fragment of another ship's passenger list containing information for six families. Of these six, five families purchased more than four freights. Using the information in the appropriate probability distribution for the St. Andrew, calculate the probability that at least five of six German immigrant families purchased more than four freights. Does it seem likely that these families came from a population similar to that of the Germans on board the St. Andrew? Explain.

6. Summarize your findings in a report. Discuss any assumptions made throughout this analysis. What are the consequences to your calculations and conclusions if your assumptions are subsequently determined to be invalid?

Throughout the picturesque valleys of mid-18th-century Germany echoed the song of the Neuländer (newlander), enticing journeymen who struggled to feed their families with the dream and promise of colonial America. The typical Neuländer sought to sign up several families from a village for immigration to a particular colony. By registering a group of neighbors, rather than isolated families, the agent increased the likelihood that his signees would not stray to the proposals of a competitor. Additionally, by signing large groups, the Neuländer fattened his purse, to the tune of one to two florins a head.

Generally, the Germans who chose to undertake the hardship of a trans-Atlantic voyage were poor, yet the cost of such a voyage was high. Records from a 1753 voyage indicate that the cost of an adult fare (one freight) from Rotterdam to Boston was 7.5 pistoles. Children aged 4 to 13 were assessed at half the adult rate (one-half freight) and those under 4 were not charged. To get a sense of the expense involved, an adult fare is equivalent to approximately $2000! Many immigrants did not have the necessary funds to purchase passage and, determined to make the crossing, paid with years of indentured servitude.

As a historian studying the influence of these German immigrants on colonial America, Hans Langenscheidt is interested in describing various demographic characteristics of these people. Unfortunately, accurate records are rare. He has discovered a partially reconstructed 1752 passenger list for a ship, the St. Andrew, containing the names of the heads of families, a list of family members traveling, their parish of origin, and the number of freights each family purchased. Unfortunately, some data are missing for some families. Langenscheidt believes that the demographic parameters of this passenger list are likely to be similar to those of the other voyages taken from Germany to America during the mid-18th century. Assuming that he is correct, he believes that it is appropriate to create a discrete probability distribution for a number of demographic variables for this population of German immigrants, presented below.

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Probability Distributions for German Immigrants on Board the 1752 Voyage of the St. Andrew Known Number of People in a Family Families per Parish Number of Families per Parish Freights Purchased Probability Number of Freights Probability Number in Family Probability 1. 0.706 0.075 0.322 1.5 0.176 0.025 0.186 3 0.425 0.150 0.000 0.136 2.5 4 0.059 0.102 0.051 0.000 0.125 3.5 6. 0.059 0.100 0.136 0.050 0.034 8. 0.025 0.017 6. 0.025 0.016