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Introductory Statistics:
Exploring the World through Data, 1e
by Gould and Ryan
Chapter 6: Modeling Random Events:
The Normal and Binomial Models
© 2013 Pearson Education, Inc.
Slide 6 - 1
A probability distribution, sometimes
called a probability distribution function
(pdf) tells us
A.
all the possible
outcomes of a random
experiment
B.
the probability of each
outcome
C.
Both A and B above
D.
None of the above
© 2013 Pearson Education, Inc.
25%
A.
25%
25%
B.
C.
25%
D.
Slide 6 - 2
True or False
Discrete outcomes (or discrete variables) are
numerical values that you can list or count.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 3
True or False
Continuous outcomes (or continuous
variables) cannot be listed or counted because
they occur over a range.
50%
50%
A.
B.
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 4
Discrete Probability distributions can be
A.
tables.
B.
graphs.
C.
equations.
D.
All of the above.
25%
A.
© 2013 Pearson Education, Inc.
25%
25%
B.
C.
25%
D.
Slide 6 - 5
True or False
The probabilities for a continuous-valued
random experiment are represented as areas
under curves, and are called a probability
density curves.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 6
True or False
One reason the Normal model is the most
widely used probability model for continuous
numerical variables is that many numerical
variables in which researchers have
historically been interested have distributions
for which the Normal model provides a very
50%
50%
close fit.
A.
B.
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 7
Which of the following represent a
Normal
Curve (or Normal Distribution)?
A.
B.
C.
D.
© 2013 Pearson Education, Inc.
25%
A.
25%
25%
B.
C.
25%
D.
Slide 6 - 8
True or False
The Normal distribution is symmetric and unimodal
(“bell-shaped”).
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 9
True or False
Because the Normal distribution is symmetric,
the mean is in the exact center of the
distribution.
50%
50%
A.
B.
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 10
In the normal curve, if the standard
deviation is large, then the Normal
curve is
25%
25%
25%
25%
A.
wide and low
B.
narrow and tall
C.
wide and tall
D.
narrow and low
A.
© 2013 Pearson Education, Inc.
B.
C.
D.
Slide 6 - 11
In the normal curve, if the standard
deviation is small, then the Normal
curve is
25%
25%
25%
25%
A.
wide and low
B.
narrow and low
C.
wide and tall
D.
narrow and tall
A.
© 2013 Pearson Education, Inc.
B.
C.
D.
Slide 6 - 12
When you are finding probabilities with
Normal models, the first and most helpful
step is to
25%
A.
sketch the curve
B.
label it appropriately
C.
shade in the region of
interest
D.
All of the above in that
order
A.
© 2013 Pearson Education, Inc.
25%
25%
B.
C.
25%
D.
Slide 6 - 13
True or False
The standard Normal model has a mean of 1
and a standard deviation of 0.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 14
True or False
The standard Normal model is an important
concept, because it allows us to find probabilities
for any Normal model.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 15
To convert a value to its z-score,
A.
B.
Subtract the standard
deviation, then divide by the25%
mean.
25%
25%
B.
C.
25%
Add the mean, then divide
by the standard deviation.
C.
Use the formula z 
D.
None of the above.
x

.
A.
© 2013 Pearson Education, Inc.
D.
Slide 6 - 16
To find the measurement from the percentile
A.
find the z-score from the
percentile, then convert the 25%
percentile to proper units.
B.
find the z-score from the
percentile, then convert the
z-score to proper units.
C.
convert the z-score to
proper units, then convert
the percentile to a z-score.
D.
None of the above.
© 2013 Pearson Education, Inc.
A.
25%
25%
B.
C.
25%
D.
Slide 6 - 17
To convert a z-score to proper units
A.
multiply the z-score times
the mean and add the result
to the standard deviation. 25%
B.
multiply the z-score times
the standard deviation and
add the result to the mean.
C.
multiply the mean times
standard deviation and add
the result to the z-score.
D.
None of the above.
A.
© 2013 Pearson Education, Inc.
25%
25%
B.
C.
25%
D.
Slide 6 - 18
True or False
The Normal model is appropriate if it produces
results that match what we see in real life.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 19
True or False
The binomial probability model is useful in
many situations with discrete-valued numerical
variables (typically counts, whole numbers).
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 20
True or False
A characteristic of a binomial model is that the
number of trials is variable.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 21
True or False
A characteristic of a binomial model is that
only two outcomes are possible at each trial.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 22
True or False
A characteristic of a binomial model is that the
probability of success is the same at each trial.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 23
True or False
A characteristic of a binomial model is that the
trials are dependent.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 24
Which of the following is a binomial
experiment?
A.
Record the number of different eye colors
in a group of 50 randomly selected
people.
B.
A married couple decides to have
children until a girl is born, but to stop at 25%
five children if they do not have any girls.
How many children will the couple have?
C.
A student guesses on every question of a
test that has 10 multiple-choice
questions. Record the number of
questions the student gets right.
D.
None of the above.
A.
© 2013 Pearson Education, Inc.
25%
25%
B.
C.
25%
D.
Slide 6 - 25
True or False
The shape of a binomial distribution depends
on both n and p.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 26
True or False
Binomial distributions are symmetric when p =
0.5, but they are also symmetric when n is
large, even if p is close to 0 or 1.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 27
True or False
For a binomial experiment the mean is
µ = np
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 28
True or False
For a binomial experiment the standard
deviation is
  np 1 p 
A.
B.
50%
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 29
True or False
For a binomial experiment the mean is
sometimes called the expected value because
if you were to carry out a binomial experiment
you would expect about µ successes.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 30
True or False
For a binomial experiment, although we expect
µ successes, we usually get µ give or take
some amount. That give-or-take amount is
what is measured by σ.
50%
A.
B.
50%
True
False
A.
© 2013 Pearson Education, Inc.
B.
Slide 6 - 31