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Based on the past results found in the Information Please Almanac , there is a 0.1809 probability that a baseball World Series contest will last four...

Based on the past results found in the
Information Please Almanac
, there is a 0.1809 probability that a
baseball World Series contest will last four games, a 0.2234 probability that it will last five games, a
0.2234 probability that it will l
ast six games, and a 0.3723 probability that it will last seven games.
a. Draw
the table of the
probability distribution for this information.
b. Is this a valid probability distribution?
Support your conclusion!
c. Find μ and σ
for the probability distribution
(show all work)
.
d. Is it unusual for a team to “sweep” by winning in four games?
2
2. Nine percent of men are color blind, which affects their ability to distinguish between colors red
and
green (problematic if you’re driving). Suppose six men are randomly selected for a study of traffic signal
perceptions and tested
.
a. Show that this is a binomial distribution (must mention all 4 conditions). Identify n, p, and q.
b. Find
the
probability that exactly two of them cannot distinguish between red and green.
3. A store has experienced a 3.2% rate of customer complaints and attempts to lower this rate by
retraining its’ employees. After the training program, 850 custom
ers are tracked.
a.
Assuming the training had
no effect
, find the mean and standard deviation for the number of
complaints in such groups of 850.
b.
It is found that only 7 of the 850 customers filed complaints. Based on the results from (a), is
t
he result of seven complaints “unusual”? Would you say the retraining program was effective?
3
4. Find the following probabilities for the standard normal distribution. Show any calculator commands.
Draw a
sketch
.
a.
)
25
.
(

z
P
b.
)
3
3
(



z
P
c.
)
45
.
2
(

z
P
5. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard
deviation of 15. Find the probability that a randomly sel
ected adult
has an IQ between 125
and 1
55
.
Draw a
Sketch.
Indicate any Calculator commands used.
)
155
125
(


x
P
=
4
6.
The US Marine Corps requires that men have heights between 64 in. and 80 in. Assume that men’s
heights are normally distributed with a
mean of 69.0 in. and a standard deviation of 2.8 in.
Draw
sketches for a and b.
a.
Find the percentage of men who meet the height requirements. Are many men denied the
opportunity to become a Marine because they do not satisfy the height requirement?
b.
If the height requirements are changed so that all men are eligible except the shortest 3%
and the tallest 4%, what are the new height requirements?
5
7
. Under
the
rules
of magic
,
flying
busses
have
to estimate
the weight of a passenger as
175 pounds.
Men
(or wizards in this case)
have weights that are normal
ly distributed with a mean of 172 pounds and a
standard deviation of 29 pounds.
Draw a sketch
for a and b
.
a.
If 1
adult male is randomly selected
,
find the probability that his weight is greater than 175
pounds.
b.
If a
flying bus
is full of 213 adult male passengers, find the probability that the mean
passenger weight
is greater than 175 pounds.
c.
Which
result
is more applicable?
All magic aside,
d
oes a pilot
of a flying bus
have to
be
concerned about exceeding this weight limit?
6
8
.
If a continuous
uniform
distribution has parameters of
2.4 1.7
and


, then the minimum is
0.5

and the maximum is 5.3.
a.
Draw a
sketch
of this distribution, labeling a
xes.
b.
For this
uniform
distribution, find
(0 1.5)
Px

9
.
A Pew Research Center poll included 1708 randomly selected adults who were asked whether “global
warming is a problem that requires immediate government action.” Results s
howed that 939 of those
surveyed indicated that immediate government action is required. A news reporter wants to determine
whether these survey results constitute strong evidence that the majority (more than 50%) of people
believe that immediate governme
nt action is required.
a.
What is the best point estimate of the proportion of adults who believe that immediate government
action is required?
b.
Construct a 97% confidence interval estimate of the proportion of adults believing that
immediate
government acti
on is required.
c.
Is there strong evidence supporting the claim that the majority is in favor of immediate
government action? Why or why not?

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