Module 3 Homework Assignment
MAT130: Beginning Statistics
Grant Smith
Professor Riccobono
October 29th 2010
Homework Assignment 3
MAT 130: Beginning Statistics
Please answer the following questions thoroughly:
Section 4-2: Basic Skills and Concepts
1. Interpreting Probability: Based on recent results, the probability of someone in
the United States being injured while using sports or recreation equipment is 1/500
(based on data from Statistical Abstract of the United States). What does it mean
when we say that the probability is 1/500? Is such an injury unusual?
1. Since the probability is so small then the injury is unusual. These
injuries occur only one in 500. 500 people out of the whole population
of Americans is a small number. If the injuries were 1/20 then the
injury would be much usual, since it would be a greater chance in
being injured while using sports or recreation equipment.
2. U.S. Senate: The 110th Congress of the United States included 84 male Senators
and 16 female Senators. If one of these Senators is randomly selected, what is the
probability that a woman is selected? Does s probability agree with a claim that men
and women have the same chance of being elected as Senators?
1. The probability that a woman is selected is .16. Men and women do
not have the same chance of being elected as senators since .16 is no
where near .50. if there was 100 senators and 50 were men and 50
were women then men and women would have the same chance of
being elected as Senators. It appears that men have a higher chance
of being elected Senator.
Section 4-6: Basic Skills and Concepts
1. Simulating Dice: When two dice are rolled, the total is between 2 and 12 inclusive.
A student simulates the rolling of two dice by randomly generating numbers between
2 and 12. Does this simulation behave in a way that is similar to actual dice? Why or
why not?
1. No. The generated numbers between 2 and 12 would be equally
likely. However they are not equally likely with real dice. Real dice
can generate numbers other than 2 and 12.
Section 4-7: Basic Skills and Concepts
1. Permutations and Combinations: What is the basic difference between a situation
requiring application of the permutations rule and one that requires the combinations
rule?
1. Permutations are different orderings of the same items that are
counted separately. For example ABC can be arranged six different
ways: ABC ACB BAC BCA CAB CBA. However combinations are not
counted separately.
Chapter 4 Statistical Literacy and Critical Thinking
1. Predicting Lottery Outcomes: A columnist for the Daily News in New York City
wrote about selecting lottery numbers. He stated that some lottery numbers are
more likely to occur because they haven't turned up as much as they should, and
they are overdue. Is this reasoning correct? Why or why not? What principle of
probability is relevant here?
1. Past drawings have no effect on the probability of future outcomes,
since the balls are replaced back into the mix. There is no way to
product which numbers are more likely or less likely to occur. The
principle of independence would be applied here.
Section 5-2: Basic Skills and Concepts
1. Random Variable: What is a random variable? A friend of the author buys one
lottery ticket every week in one year. Over the 52 weeks, she counts the number of
times that she won something. In this context, what is the random variable, and
what are its possible values?
1. A random variable is a variable that has a single numerical value. This
is determined by chance. The possible values is 0,1,2,3,4,.....50,51,52
2. Expected Value: A researcher calculates the expected value for the number of girls
in three births. He gets a result of 1.5. He then rounds the result to 2, saying that it
is not possible to get 1.5 girls when three babies are born. Is this reasoning correct?
Explain.
1. There is no requirement that the expected value must be an integer.
So the correct expected value is 1.5 not 2. This would be the mean
value in many trials not just one. Therefore it is possible to have 1.5
as a reasonable possibility.
Section 5-5: Basic Skills and Concepts
1. Poisson Distribution: What are the conditions for using the Poisson distribution?
1. Variable x is the occurrence of a certain event over some interval
(such as time). The occurrences are random, independent of each
other and are distributed over the interval. Example you would want
to find out how many earthquakes happen over a number of years. If
there was 72 earthquakes in 100 years you would divide 72 over 100
and find the mean per year was .72 Then you would use the formula
(5.9 in the textbook) to find out how many happen in 1 year, or two
years ect....
Chapter 5 Statistical Literacy and Critical Thinking
1. Random Variable: What is a random variable? Is it possible for a discrete random
variable to have an infinite number of possible values?
1. Random variable is a variable that has a single numerical outcome,
that is determined by chance for each outcome of a procedure. It is
possible for a discrete random variable to have an infinite number of
values.
2. Discrete versus Continuous: What is the difference between a discrete random
variable and a continuous random variable?
1. Discrete random variable has either a finite number of values or a
countable number of values and they can be associated with a
counting process, so that the number of values is 0 or 1 or 2 or 3 etc..
Whereas continuous random variables have infinite values, and these
values can be associated with measurements on a continuous scale
without gaps or interruptions.
2. For example discrete random variable would be the number of eggs
that a hen lays in a day. This would be either zero eggs or five eggs or
20 eggs. A hen cannot lay 2.67 eggs or 50.3 eggs. It would be a solid
number. Continuous random variable would be the amount that a cow
produced in milk a day. Could be between 0 and 7 gallons of milk. Or
the cow could produced 10.256 gallons. It would not be restricted to
a solid number.