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The Voyage of the St. Andrew
Throughout the picturesque valleys of mid-18th-century Germany echoed
the song of the neuländer (newlander). Their song enticed journeymen
who struggled to feed their families with the dream and promise of colonial
America. Traveling throughout the German countryside, 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 equally enticing
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 pistole. Children between the
ages of four and thirteen were assessed at half the adult rate (one-half
freight). Children under four were not charged. To get a sense of the expense
involved, it has been estimated that the adult fare, 7.5 pistoles, is
equivalent to approximately $2000 (1998 U.S.)! For a large family, the cost
could easily be well beyond their means. Even though many immigrants did
not have the necessary funds to purchase passage, they were determined to
make the crossing.Years of indentured servitude for themselves and other
family members was often the currency of last resort.
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. In his research, he has discovered a partially reconstructed 1752 passenger
list for a ship, the St.Andrew.This list contains the names of the head of families,
a list of family members traveling with them, their parish of origin, and the
number of freights each family purchased. Unfortunately, some of the data are
missing for some of the families. Langenscheidt believes that the demographic
parameters of this passenger list are likely to be similar to those of the other numerous
voyages taken from Germany to America during the mid-eighteenth
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. His distributions are presented below.
Probability Distribution of the
Number of Families per Parish of
German Immigrants on Board the
1752 Voyage of the St. Andrew
Number of
Families per Parish Probability
1 0.706
2 0.176
3 0.000
4 0.059
5 0.000
6 0.059 CASE STUDY
SullStatCH06_Fpp324-377 11/20/02 10:51 AM Page 374
1. Using the information above, describe, through histograms and numerical
summaries such as the mean and standard deviation, each of the
probability distributions.
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 of the 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 1998 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.
This fragment listed information for six families. Of these six, five families
purchased more than four freights. Using the information contained
in the appropriate probability distribution for the St. Andrew,
calculate the probability that at least five of six German immigrant
families would have 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? 375
Probability Distribution of the
Known Number of Freights
Purchased by the German
Families on Board the 1752
Voyage of the St. Andrew
Number
of Freights Probability
1.0 0.075
1.5 0.025
2.0 0.425
2.5 0.150
3.0 0.125
3.5 0.100
4.0 0.050
5.0 0.025
6.0 0.025
Probability Distribution of the
Known Number of People in a
Family for the Germans on Board
the 1752 Voyage of the St. Andrew
Number
in Family Probability
1 0.322
2 0.186
3 0.136
4 0.102
5 0.051
6 0.136
7 0.034
8 0.017
9 0.016
Data Source: Wilford W. Whitaker and Gary T. Horlacher, Broad Bay Pioneers (Rockport,
Maine: Picton Press, 1998), 63–68. Distributions created from the partially reconstructed 1752
passenger list of the St. Andrew presented by Whitaker and Horlacher.
SullStatCH06_Fpp324-377 11/20/02 10:51 AM Page 375
376
Should We Convict?
In 1964, a woman who was shopping in Los Angeles had her purse stolen by
a young, blonde female who was wearing a ponytail. The blonde female got
into a yellow car that was driven by a black male who had a mustache and a
beard.The police located a blonde female named Janet Collins who wore her
hair in a ponytail and had a friend who was a black male who had a mustache
and beard and also drove a yellow car.The police arrested the two subjects.
Because there were no eyewitnesses and no real evidence, the prosecution
used probability to make its case against the defendants. The following
probabilities were presented by the prosecution for the known characteristics
of the thieves:
DECISIONS
(a) Assuming that the characteristics listed above are independent of each
other, what is the probability that a randomly selected couple would
have all these characteristics? That is, what is P (“yellow car” and “man
with a mustache” and and “interracial couple in a car”)?
(b) Would you convict the defendants based on this probability? Why?
(c) Now let n represent the number of couples in the Los Angeles area that
could have committed the crime. Let p represent the probability a randomly
selected couple would have all six characteristics listed above.
Let the random variable X represent the number of couples that have
all the characteristics listed in the table. Assuming that the random
variable X follows the binomial probability function, we have
Assuming that there were couples in the Los Angeles
area, what is the probability that more than one of them have the characteristics
listed in the table? Does this result cause you to change your
mind regarding the defendants’ guilt?
(d) Now, let’s look at this case from a different point of view.We will compute
the probability that more than one couple has the characteristics
described, given that at least one couple has the characteristics:
Conditional Probability Rule
Compute this probability, assuming Compute this probability
again, but this time assume that Do you think that
the couple should be convicted “beyond all reasonable doubt”? Why?
n = 2,000,000.
n = 1,000,000.
=
P1X 7 12
P1X Ú 12
P1X 7 1|X Ú 12 =
P1X 7 1 and X Ú 12
P1X Ú 12
n = 1,000,000
P1X = x2 = nCx # px11 - p2n-x, x = 0, 1, 2, Á , n.
Á
Characteristic Probability
Yellow car 1/10
Man with a mustache
Woman with a ponytail 1/10
Woman with blonde hair 1/3
Black man with beard 1/10
Interracial couple in car 1/1000
14
SullStatCH06_Fpp324-377 12/10/02 11:53 AM Page 376
Quality Assurance in Customer Relations
377
The Customer Relations Department at Consumers
Union (CU) receives thousands of letters and e-mails
from customers each month. Some people write in asking
how well a product performed during CU’s testing, some
people write in sharing their own experiences with their
household products, and the remaining people write in
for an array of other reasons. In order to be able to respond
to each letter and e-mail that is received, Customer
Relations recently upgraded its customer contact
database. Although much of the process has been automated,
it still requires employees to manually draft the
responses. Given the current size of the department, each
Customer Relations representative is required to draft
approximately 300 responses each month.
As part of a quality assurance program, the Customer
Relations manager would like to develop a plan
that allows him to evaluate the performance of his employees.
From past experience, he knows that the
probability a new employee will write an initial draft
of a response that contains errors is approximately
10%. The manager would like to know how many of
the 300 responses he should sample in order to have a
cost effective quality assurance program.
(a) Let X be a discrete random variable that represents
the number of the draft responses
that contain errors. Describe the probability distribution
for X. Be sure to include the name of the
probability distribution, possible values for the
random variable X, and values of the parameters.
n = 300
(b) To be effective, suppose the manager would like to
have a 95% probability of finding at least one draft
document that contains an error.Assuming that the
probability a draft document will have errors is
known to be 10%, determine the appropriate sample
size to satisfy the manager’s requirements. Hint:
We are required to find the number of draft documents
that must be sampled so that the probability
of finding at least one document containing an
error is 95%. In other words, we need to determine
n by solving:
(c) Suppose the error rate is really 20%.What sample
size will the manager need to review to have a
95% probability of finding one or more documents
containing an error?
(d) Now, let Y be a discrete random variable that represents
the number of errors discovered in a single
draft document. (It is possible for a single draft to
contain more than one error.) The manager determined
that errors occurred at the rate of 0.3 errors
per document. Describe the probability distribution
for Y. Be sure to include the name of the
probability distribution, possible values for the
random variable Y, and values of the parameters.
(e) What is the probability that a document contains
no errors? One error? At least two errors?
Note to Readers: In many cases, our test protocol and analytical
methods are more complicated than described in these examples.
The data and discussions have been modified to make the material
more appropriate for the audience.
P1x Ú 12 = 0.95.
SullStatCH06_Fpp324-377 11/20/02 10:51 AM Page 377
Solution Description

**Question 1**

__HISTOGRAM SHOWING PROBABILITY DISTRIBUTION OF THE NUMBER OF FAMILIES PER PARISH OFGERMAN IMMIGRANTS.__