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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