Deck 4: Randomness and Probability

Question 1

A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads
On the next flip is

A) less than 50%, since "tails" is due to come up.
B) greater than 50%, since it appears that we are in a streak of "heads."
C) It cannot be determined.
D) 50%.

Answer 1

D

Question 2

BatCo, a company that sells batteries, claims that 99.5% of their batteries are in working order. How
Many would you expect to buy, on average, to find one that does not work?

A) 5
B) 995
C) 2000
D) 200
E) 100

Answer 2

D

Question 3

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to
the bike. 34% of the bikes sold have both features.
Given that a randomly selected bike has a kickstand, what are the chances that it also has a water
Bottle holder?

A) 21%
B) 61.8%
C) 34%
D) 26%
E) 56.7%

Answer 3

B

Question 4

In a stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of
students eat breakfast and also floss their teeth.
What is the probability that a student from this class eats breakfast or flosses?

A) 34%
B) 11%
C) 9%
D) 91%
E) 57%

Question 5

On a physical fitness test middle school boys are awarded one point for each push-up they can do,
And a point for each sit-up. National results showed that boys average 18 pushups with a standard
Deviation of 4 push-ups, and 34 sit-ups with standard deviation 11. The mean of their combined
(total) scores was therefore 18 + 34 = 52 points. What is the standard deviation of their combined
Scores?

A) 137
B) 11.7
C) 5.3
D) cannot be determined
E) 15

Question 6

A friend of yours plans to toss a fair coin 200 times. You watch the first 40 tosses, noticing that she
Got only 16 heads. But then you get bored and leave. If the coin is fair, how many heads do you
Expect her to have when she has finished the 200 tosses?

A) 100
B) 116
C) 92
D) 96
E) 80

Question 7

A supermarket claims that their checkout scanners correctly price 99.8% of the items sold. How
Many items would you expect to buy, on average, to find one that scans incorrectly?

A) 998
B) 500
C) 200
D) 99.8
E) 2

Question 8

Political analysts estimate the probability that Candidate A will run for president in the next
Election is 45%, and the probability that Candidate B will run is 20%. If their political decisions are
Independent, then what is the probability that only Candidate A runs for president?

A) 36%
B) 45%
C) 25%
D) 11%
E) 9%

Question 9

A survey of some AP* Stats students recorded gender and whether the student was left or
Right-handed. Results were summarized in a table like the one shown. If it turned out that
Handedness was independent of gender, how many of the AP* Stats students were lefty girls?

A) 7
B) 4
C) 9
D) 10
E) cannot be determined

Question 10

According to the National Telecommunication and Information Administration, 50.5% of U.S.
Households had Internet access in 2001. What is the probability that four randomly selected U.S.
Households all had Internet access in 2001?

A) 12.6%
B) 93.5%
C) 49.5%
D) 6.5%
E) 50.5%

Question 11

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to
the bike. 34% of the bikes sold have both features.
What is the probability that a randomly selected bicycle will have a kickstand or a water bottle
Holder?

A) 81%
B) 34%
C) none of these
D) 56.7%
E) 61.8%

Question 12

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift.
If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)

A) 37.2, 2.24
B) 36, 3.14
C) 36, 8.88
D) none of these
E) 37.2, 6.34

Question 13

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to
the bike. 34% of the bikes sold have both features.
We can tell that these two features are independent because…

A) These two features don't have anything to do with each other, so we know they're independent.
B) The probability of having a kickstand given that you have a water bottle (56.7%) is about equal to the probability of having a kickstand (55%).
C) The probability of having both features (34%) does not equal the probability of having neither feature (19%).
D) The probability of having both features is not zero; it is 34%.
E) The probability of having either feature (81%) doesn't equal the probability of having just one feature (60% and 55%).

Question 14

Which of these random variables has a binomial model?

A) The number of girls a family has out of the three children they will have.
B) The number of books we select out of a pile of 9 books that are non-fiction.
C) none of these
D) The number of children a family has until they have two boys.
E) The number of times a free throw is shot until one shot is made.

Question 15

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift.
If the workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?

A) $45
B) none of these
C) $180
D) $4.65
E) $46.50

Question 16

Which of these random variables has a geometric model?

A) The number of Democrats among a group of 20 randomly chosen adults.
B) The number of aces among the top 10 cards in a well-shuffled deck.
C) The number of cars inspected until we find three with bad mufflers.
D) The number of people we check until we find someone with green eyes.
E) The number of cards of each suit in a 10-card hand.

Question 17

Five juniors and four seniors have applied for two open student council positions. School
Administrators have decided to pick the two new members randomly. What is the probability they
Are both juniors or both seniors?

A) 0.444
B) 0.395
C) 0.569
D) 0.506
E) 0.722

Question 18

The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a
Committee, what is the probability these chairpersons are the same gender?

A) 5/9
B) 7/8
C) 4/9
D) 1/2
E) 5/8

Question 19

In a large 2lb. bag of candies (the true fun size!) 15% of the candies are green. The chances of
Pulling out at least one green candy in three tries is…

Question 20

If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances
Of rolling exactly three successes?

A) 16.67%
B) 33.33%
C) 32.15%
D) none of these
E) 0.32%

Question 21

Which two events are most likely to be independent?

A) doing the Statistics homework; getting an A on the test
B) registering to vote; being left-handed
C) having 3 inches of snow in the morning; being on time for school
D) having a car accident; having a junior license
E) being a senior; going to homeroom

Question 22

A friend of yours plans to toss a fair coin 200 times. You watch the first 20 tosses and are surprised
That she got 15 heads. But then you get bored and leave. How many heads do you expect her to
Have when she has finished all 200 tosses?

A) 115
B) 110
C) 105
D) 150
E) 100

Question 23

A poll of 120 Ithacans found that 30 had visited the Museum of the Earth, and that 80 had been to
Home Depot. If it appeared that going to Home Depot and going to the Museum of the Earth were
Independent events, how many of those polled had been to both?

A) 20
B) It cannot be determined.
C) 15
D) 10
E) 24

Question 24

The length of a cat's tail is roughly normally distributed with a mean of 5" and a standard deviation
Of 2". The probability of having a cat with a 3.5" tail or shorter is…

A) 77.3%
B) 75%
C) 25%
D) none of these
E) 22.7%

Question 25

Which of these has a geometric model?

A) The number of people we survey until we find someone who owns an iPod.
B) The number of black cards in a 10-card hand.
C) The colors of the cars in the grocery store parking lot.
D) The number of cards drawn from a deck until we find all four aces.
E) The number of hits a baseball player gets in 6 times at bat.

Question 26

Which of these is most likely to have a binomial model?

A) The colors of the cars in the grocery store parking lot.
B) The number of cards drawn from a deck until we find all four aces.
C) The number of hits a baseball player gets in 6 times at bat.
D) The number of black cards in a 10-card hand.
E) The number of people we survey until we find someone who owns an iPod.

Question 27

Which of these has a Binomial model?

A) the number of people we survey until we find two people who have taken Statistics
B) the number of aces in a five-card Poker hand
C) the number of sodas students drink per day
D) the number of people we survey until we find someone who has taken Statistics
E) the number of people in a class of 25 who have taken Statistics

Question 28

Pepsi is running a sales promotion in which 12% of all bottles have a "FREE" logo under the cap.
What is the probability that you find two free ones in a 6-pack?

A) 97%
B) 13%
C) 23%
D) 1%
E) 11%

Question 29

If my dresser drawer has 10 blue socks and 12 black socks and I randomly pull out two socks, what
Are the chances that they are both black?

A) none of these
B) 27.3%
C) 29.8%
D) 52%
E) 28.6%

Question 30

Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding
And 9% for going through a red light. If 4% have been ticketed for both, what is the probability that
A teenage driver has been issued a ticket for speeding but not for running a red light?

A) 12%
B) 8%
C) 13%
D) 17%
E) 3%

Question 31

Which of these has a Geometric model?

A) the number of sodas students drink per day
B) the number of people we survey until we find two people who have taken Statistics
C) the number of aces in a five-card Poker hand
D) the number of people in a class of 25 who have taken Statistics
E) the number of people we survey until we find someone who has taken Statistics

Question 32

Six Republicans and four Democrats have applied for two open positions on a planning committee.
Since all the applicants are qualified to serve, the City Council decides to pick the two new
Members randomly. What is the probability that both come from the same party?

Question 33

Which of these random variables is most likely to have a binomial model?

A) The number of aces among the top 10 cards in a well-shuffled deck.
B) The number of people we check until we find someone with green eyes.
C) The number of Democrats among a group of 20 randomly chosen adults.
D) The number of cars inspected until we find three with bad mufflers.
E) The number of cards of each suit in a 10-card hand.

Question 34

Some marathons allow two runners to "split" the marathon by each running a half marathon. Alice
And Sharon plan to split a marathon. Alice's half-marathon times average 92 minutes with a
Standard deviation of 4 minutes, and Sharon's half-marathon times average 96 minutes with a standard deviation of 2 minutes. Assume that the women's half-marathon times are independent.
The expected time for Alice and Sharon to complete a full marathon is 92 + 96 = 188 minutes. What
Is the standard deviation of
Their total time?

A) 2 minutes
B) 20 minutes
C) 6 minutes
D) It cannot be determined.
E) 4.5 minutes

Question 35

Which two events are most likely to be independent?

A) being a senior, and leaving campus for lunch
B) having a flat tire, and being late for school
C) having a driver's license, and having blue eyes
D) having a car accident, and having 3 inches of snow today
E) getting an A in math, and getting an A in Physics

Question 36

According to the National Telecommunication and Information Administration, 56.5% of U.S.
Households owned a computer in 2001. What is the probability that of three randomly selected U.S.
Households at least one owned a computer in 2001?

A) 56.5%
B) 82.0%
C) 43.5%
D) 91.8%
E) 18.0%

Question 37

A national study found that the average family spent $422 a month on groceries, with a standard
Deviation of $84. The average amount spent on housing (rent or mortgage) was $1120 a month,
With standard deviation $212. The expected total a family spends on food and housing is 422 + 1120
= $1542. What is the standard deviation of the total?

A) $128
B) cannot be determined
C) $228
D) $148
E) $295

Question 38

In a stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of
students eat breakfast and also floss their teeth.
What is the probability that a student from this class eats breakfast but does not floss?

A) 34%
B) 91%
C) 57%
D) 9%
E) 11%

Question 39

An ice cream stand reports that 12% of the cones they sell are "jumbo" size. You want to see what a
"jumbo" cone looks like, so you stand and watch the sales for a while. What is the probability there
Is exactly 1 jumbo among the first 6 cones sold by the ice cream stand?

A) 84%
B) 54%
C) 6%
D) 12%
E) 38%

Question 40

An ice cream stand reports that 12% of the cones they sell are "jumbo" size. You want to see what a
"jumbo" cone looks like, so you stand and watch the sales for a while. What is the probability that
The first jumbo cone is the fourth cone you see them sell?

A) 93%
B) 8%
C) 60%
D) 33%
E) 40%

Question 41

A young boy is fishing off the end of a dock. He estimates that for one out of every 15 times he casts his line, he gets at least a
nibble from a curious fish. He is going to cast his line 50 times before he switches to toad hunting.
If he gets only 5 nibbles on his line, is that a signal that he is having less success than usual?
Justify your answer.

Question 42

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue and 10 of his most favorite color, neon orange.
What is the probability that if he removes 2 marbles without looking, that he will get two
orange marbles?

Question 43

Surprised by the low number of Type B blood donors at the blood drive, the American Red
Cross wonders if the 11% estimate was too high for your area. How many Type B blood
donors would it take to convince you that this estimate might be too high? Justify your
answer.

Question 44

A survey of local car dealers revealed that 64% of all cars sold last month had CD players,
28% had alarm systems, and 22% had both CD players and alarm systems.
a. What is the probability one of these cars selected at random had neither a CD player nor
an alarm system?
b. What is the probability that a car had a CD player unprotected by an alarm system?
c. What is the probability a car with an alarm system had a CD player?
d. Are having a CD player and an alarm system disjoint events? Explain.

Question 45

A biology professor responds to some student questions by e-mail. The probability model
below describes the number of e-mails that the professor may receive from students
during a day.
a. How many e-mails should the professor expect to receive each day?
b. What is the standard deviation?
c. If it takes the professor an average of ten minutes to respond to each e-mail, how much
time should the professor expect to spend responding to student e-mails each day?

Question 46

Annual review You are up for your annual job performance review. You estimate there's a
30% chance you'll get a promotion, a 40% chance of a raise, and a 20% chance of getting
both a raise and a promotion.
a. Find the probability that you get a raise or promotion.
b. Are the raise and the promotion independent events? Explain.

Question 47

A survey of families revealed that 58% of all families eat turkey at holiday meals, 44% eat
ham, and 16% have both turkey and ham to eat at holiday meals.
a. What is the probability that a family selected at random had neither turkey nor ham at
their holiday meal?
b. What is the probability that a family selected at random had only ham without having
turkey at their holiday meal?
c. What is the probability that a randomly selected family having turkey had ham at their
holiday meal?
d. Are having turkey and having ham disjoint events? Explain.

Question 48

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue and 10 of his most favorite color, neon orange.
If Jacob removes 3 marbles from the bag, what are the chances that he will get at least one
orange?

Question 49

The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only
5% of the customers buy a magazine and thinks that he might be able to use the display space to sell something more
profitable. Before making a final decision he decides that for one day he'll keep track of the number of customers and
whether or not they buy a magazine.
What is the probability that exactly 2 of the first 10 customers buy magazines? Show work.

Question 50

The American Veterinary Association claims that the annual cost of medical care for dogs
averages $100 with a standard deviation of $30, and for cats averages $120 with a standard
deviation of $35.
a. Find the expected value for the annual cost of medical care for a person who has one dog
and one cat.
b. Find the standard deviation for the annual cost of medical care for a person who has one
dog and one cat.
c. Suppose that a couple owns four dogs.
i. Find the expected value for the annual cost of medical care for the couple's dogs.
ii. Find the standard deviation for the annual cost of medical care for the couple's dogs.

Question 51

A new clothing store advertises that during its Grand Opening every customer that enters the store can throw a bouncy
rubber cube onto a table that has squares labeled with discount amounts. The table is divided into ten regions. Five regions
award a 10% discount, two regions award a 20% discount, two regions award a 30% discount, and the remaining region
awards a 50% discount. Show your work.
What is the probability that there is at least one customer to win a 50% discount among the
first five customers that enter the store?

Question 52

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your
school.
What is the probability that exactly 2 of the first 20 blood donors have Type B blood?

Question 53

Basketball player heights Assume the heights of high school basketball players are
normally distributed. For boys the mean is 74 inches with a standard deviation of 4.5
inches, while girl players have a mean height of 70 inches and standard deviation 3 inches.
At a mixed 2-on-2 tournament teams are formed by randomly pairing boys with girls as
teammates.
a. On average, how much taller do you expect the boy to be?
b. What will be the standard deviation of the difference in teammates' heights?
c. On what fraction of the teams would you expect the girl to be taller than the boy?

Question 54

A cell phone company offers a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If
you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of
customers will need the replacement voucher and 10% will request a repair.
Suppose the company collects 10 warranty plans on one day. What is the mean of the
company's total profit?

Question 55

A cell phone company offers a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If
you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of
customers will need the replacement voucher and 10% will request a repair.
If the company charges $25 for this extended warranty, what is the expected value of the
profit they will earn?

Question 56

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your
school.
How many blood donors should the American Red Cross expect to collect from until it gets
a donor with Type B blood?

Question 57

At an antique boat show, 90% of the boats are made of a natural, polished wood. 75% of the boats have some chrome accents
on the boat on at least one visible feature. And 60% have both features.
What is the probability that if a boat has chrome accents it is also made of natural wood?

Question 58

Growth A scientist is running an experiment that involves waiting for a culture to grow.
The average time for one experiment to run is 93 minutes with a standard deviation of 10
minutes.
a. If the scientist is going to run five experiments, with a 7 minute set-up time in between
each experiment, what is the average of the total time this will take?
b. What is the standard deviation of the total time?
c. What assumption did you need make the calculations in the previous two problems?

Question 59

Strange dice A game is played with 2 strange dice.
• The six faces of Die A show a 1 and five 3's.
• Die B has four 2's and two 6's.
a. Create a probability model for the total you get when you roll both dice.
b. Find the mean of the total.
c. Find the standard deviation of the total.

Question 60

A new clothing store advertises that during its Grand Opening every customer that enters the store can throw a bouncy
rubber cube onto a table that has squares labeled with discount amounts. The table is divided into ten regions. Five regions
award a 10% discount, two regions award a 20% discount, two regions award a 30% discount, and the remaining region
awards a 50% discount. Show your work.
What is the probability that the first customer to win a 30% discount is the sixth customer
that enters the store?

Question 61

Seatbelts Safety officials hope a public information campaign will increase the use of
seatbelts above the current 70% level. Their efforts include running radio and TV ads,
putting up billboards, having police officers appear on talk shows, and getting newspapers
to indicate whether people injured in accidents were belted in. After several months they
check the effectiveness of this campaign with a statewide survey of 560 randomly chosen
drivers. 407 of those drivers report that they wear a seatbelt.
a. Verify that a Normal model is a good approximation for the binomial model in this
situation.
b. Does the survey result suggest that the education/advertising campaign was effective?
Explain.

Question 62

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue and 10 of his most favorite color, neon orange.
What are the chances that he as he removes marbles from the bag, he doesn't get an orange
marble until his fourth attempt?

Question 63

Shoot You and a friend are working on shooting free throws at basketball practice. Your
friend has a season average of making 80% of his shots.
a. If the coach asks your friend to shoot 70 times, how many shots do you expect him to
make, on average?
b. What is the standard deviation of the number of shots made out of 70?
c. Your friend makes 60 out of 70 shots and is ready to tell the coach that he is improving.
The graph below shows a simulation of this distribution. Using both your answers to (a)
and (b) and this graph, explain whether or not the coach should have confidence in his
improvement.

Question 64

A new clothing store advertises that during its Grand Opening every customer that enters the store can throw a bouncy
rubber cube onto a table that has squares labeled with discount amounts. The table is divided into ten regions. Five regions
award a 10% discount, two regions award a 20% discount, two regions award a 30% discount, and the remaining region
awards a 50% discount. Show your work.
What is the probability that a customer gets less than a 20% discount?

Question 65

A sporting goods store announces a "Wheel of Savings" sale. Customers select the merchandise they want to purchase, then
at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12
regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount
and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100%
discount - the merchandise is free! Show your work.
As you wait your turn in line there are three gold winners in a row. A lively discussion
ensues between the next two customers. One thinks that streak about kills her chances of
winning free merchandise, as the wheel won't come up gold again for a very long time.
The other says that the wheel is clearly on a hot streak, so they are lucky to be next in line.
Comment on their opinions.

Question 66

The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only
5% of the customers buy a magazine and thinks that he might be able to use the display space to sell something more
profitable. Before making a final decision he decides that for one day he'll keep track of the number of customers and
whether or not they buy a magazine.
He had 280 customers that day. Assuming this day was typical for his store, what would
be the mean and standard deviation of the number of customers who buy magazines each
day?

Question 67

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4%
of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more
interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of
customers for a day, and whether they purchase specialty clothes for their pet.
The owner had 275 customers that day. Assuming this was a typical day for her store, what
would be the mean and standard deviation of the number of customers who buy specialty
clothes for their pet each day?

Question 68

At an antique boat show, 90% of the boats are made of a natural, polished wood. 75% of the boats have some chrome accents
on the boat on at least one visible feature. And 60% have both features.
What is the probability that a boat is either made of wood or has chrome accents?

Question 69

A cell phone company offers a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If
you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of
customers will need the replacement voucher and 10% will request a repair.
Is the $25 warranty a wise purchase for you? Given that you will probably buy dozens of
devices over the next decade, are these types of warranties a wise purchase for you?

Question 70

A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers
unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested
that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and
none required more than three repairs.
What is the standard deviation of the number of repairs that may be required during the
three-year term of the lease? On what assumption does your calculation rest? Do you think
this assumption is reasonable?

Question 71

A sporting goods store announces a "Wheel of Savings" sale. Customers select the merchandise they want to purchase, then
at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12
regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount
and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100%
discount - the merchandise is free! Show your work.
What is the probability that three consecutive customers all get 20% discounts?

Question 72

A cell phone company offers a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If
you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of
customers will need the replacement voucher and 10% will request a repair.
What is the standard deviation of their profit?

Question 73

A sporting goods store announces a "Wheel of Savings" sale. Customers select the merchandise they want to purchase, then
at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12
regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount
and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100%
discount - the merchandise is free! Show your work.
What is the probability that the first gold winner (100%) is the fifth customer in line?

Question 74

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4%
of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more
interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of
customers for a day, and whether they purchase specialty clothes for their pet.
What is the probability that she does not sell a garment until the 7th customer? Show work.

Question 75

Decorate A store sells ornaments for Christmas trees. The prices of the ornaments are
roughly normally distributed with a mean of $7.65 and a standard deviation of $1.45.
a. What is the probability that a randomly selected ornament will cost more than $10?
b. If eight ornaments are randomly selected, what is the probability that exactly 3 of them
cost over $10?

Question 76

Dice rolls Two players compete against each other by rolling dice - not the traditional
dice, though. One face of Alphonso's die has an 8 and the other five faces are all 2's.
Bettina's die has four 3's and two 1's on the six faces.
a. They each roll their die, and the player with the highest score wins. Which player has the
advantage? Explain.
b. If Alphonso wins, Bettina pays him $10. How much should he pay her if she wins in
order to make the game fair?
c. They decide to change the rules. They'll each roll, and the winner will collect the number
of dollars shown on his or her die. For example, If Alphonso rolls a 2 and Bettina rolls a 3,
he'll pay her $3. Create a probability model for the amount Alphonso wins.
d. Find the expected value and standard deviation of Alphonso's winnings at this game.
e. If they play this new game repeatedly which player has the advantage? Explain.

Question 77

A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers
unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested
that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and
none required more than three repairs.
The yearly service contract for the food fryer estimates a mean annual cost of $140 with a
standard deviation of $40. What is the expected value and standard deviation of the total
cost for the service contracts for the freezer and the food fryer?

Question 78

Passing the test Assume that 70% of teenagers who go to take the written drivers license
test have studied for the test. Of those who study for the test, 95% pass; of those who do not
study for the test, 60% pass. What is the probability that a teenager who passes the written
drivers license test did not study for the test?

Question 79

At an antique boat show, 90% of the boats are made of a natural, polished wood. 75% of the boats have some chrome accents
on the boat on at least one visible feature. And 60% have both features.
Does it appear that having chrome accents and being made of wood are independent
characteristics? Provide statistical evidence to justify your response.

Question 80

Carpet A store selling carpet tracks the amount of square footage sold to its customers,
rounding to the nearest 500 sq. ft. Here is the distribution.
a. What is the average expected area sold?
b. If the average cost of carpet sold is $3/sq. ft., what is the average sale price per customer?
c. If a salesman completes sales to five customers one day, what do you expect his total
sales to be?