Download 1 pt

Probability
Distributions
Mean &
Expectation
Variance &
Std. Dev.
Binomial
Distribution
(no calc)
Binomial
Distribution
(with calc)
1 pt
1 pt
1 pt
1 pt
1 pt
2 pt
2 pt
2 pt
2 pt
2 pt
3 pt
3 pt
3 pt
3 pt
3 pt
4 pt
4 pt
4 pt
4 pt
4 pt
5 pt
5 pt
5 pt
5 pt
5 pt
1
Is the following a probability distribution?
X
P(X)
0
.125
1
.375
2
.375
3
.125
2
Yes, since 0 < P(X) < 1
and
The sum of P(X) is 1
3
Joe plans to flip a coin 3 times in a
row. Let the random variable be
number of tails. Make a
probability distribution table.
4
X
P(X)
0
1/8
1
3/8
2
3/8
3
1/8
5
Fill in the missing probability:
X
1
P(X) .18
2
.21
3
.23
4
5
.21
6
.17
7
Lydia rolls one six sided die.
Create a probability distribution
in which the random variable is
the possible outcomes.
8
X
1
2
3
4
5
6
P(X)
1/6
1/6
1/6
1/6
1/6
1/6
9
Construct a probability distribution for
drawing a card from a deck of 30 cards
consisting of 14 cards numbered 1, 10
cards numbered 2, 5 cards numbered 3,
and 1 card numbered 4.
10
X
1
2
3
4
P(X)
14/30
10/30
5/30
1/30
11
Find the mean of the probability
distribution.
X
1
2
3
4
5
P(X)
.18
.21
.23
.17
.21
12
Mean = 3.02
13
A contractor has a 65% chance
of making $45,000, a 20%
chance of losing $30,000 and a
15% chance of breaking even.
What is the expected value?
14
$23,250
15
A raffle has two prizes: $500 and $100.
Each ticket costs $5. 1000 tickets are
sold and you buy 3 tickets. What is the
expected value?
16
-$13.25
17
A company manufactures calculators
in batches of 5 and there is a 5% rate
of defects. Find the mean number of
defects per batch.
18
Mean = 0.25
19
In a sample of 40 Internet users, a survey
showed that 61% are somewhat
concerned about the confidentiality of
their email. Find the mean number of
people who are NOT concerned with the
confidentiality.
20
15.6
21
Compute the variance:
X
0
1
2
3
4
P(X)
.18
.44
.27
.08
.03
22
0.92
23
Compute the standard deviation:
X
0
1
2
3
4
P(X)
0.1
0.2
0.3
0.2
0.2
24
1.25
25
A study found that 1% of Social Security
recipients are too young to vote. If 800
Social Security recipients are randomly
selected, find the variance of the number of
recipients who are too young to vote.
26
7.92
27
Find the standard deviation for the
number of heads when 20 coins are
tossed.
28
2.24
29
If 3% of calculators are defective, find
the variance and standard deviation of
a lot of 300 calculators.
30
8.73, 2.95
31
A company manufactures calculators in
batches of 5 and there is a 5% rate of
defects. Find the probability of getting
exactly 3 defects in a batch.
32
N=5
X=3
P = .05
Q = .95
P(exactly 3 heads) = .001
33
The percentage of American men who say
they would marry the same woman if they
had to do it all over again is 80%. The
percentage of American women who say they
would marry the same man again is 50%.
What is the probability that in a group of 10
married men, at least 8 will claim they would
marry the same woman again?
34
.677
35
Have you ever purchased an article of
clothing, worn it once, and then returned
it? This is called a “one-time fling”; about
10% of adults have deliberately done this
and feel no guilt. In a group of 7 adult
friends, what is the probability that no
more than 2 people have done a “one-time
fling”?
36
.974
37
In Manitoba, 5% of fish that were caught
and released died. Suppose that a group
of anglers caught and released 16 fish in
Manitoba. What is the probability that
all of the fish lived?
38
.440
39
Richard has just been given a 10-multiple
choice quiz in history class. Each question
has 5 possible answers. Assuming that
Richard guesses on all 10 questions, find
the probability that he will answer all
questions incorrectly.
40
0.107
41
A fair quarter is flipped 3 times. Find
the probability of getting exactly 3
heads.
42
.125
43
Approximately 10% of the population has
blood type B. Suppose we choose 12 people
at random from the population and test the
blood type of each. What is the probability
that exactly 3 of these people have blood
type B?
44
0.085
45
Privacy is a concern for many users of the
Internet. One survey showed that 59% of
Internet users are somewhat concerned about
the confidentiality of their e-mail. Based on
this information, what is the probability that
for a random sample of 40 users, 20 are
concerned about the privacy of their email?
46
.065
47
A social scientist claims that only
60% of all high school seniors
who are capable of doing college
work actually go to college. If this
is true, find the probability that
among 10 capable seniors, at least
8 will go to college.
48
.167
49
A research team at Cornell University
conducted a study showing that
approximately 10% of all businessmen who
wear ties wear them so tight that they
actually reduce blood flow to the brain. At
a board meeting of 20 businessmen, all of
whom wear ties, what is the probability that
no more than 3 ties are too tight?
50
.867
51