Deck 4: Displaying and Comparing Qualitative Data

Question 1

Which two events are most likely to be independent?

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

Answer 1

D

Question 2

SAT prep Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students. You overhear a classmate say he got into the college he wanted. What is the probability he didn't take an SAT prep course?

Answer 2

$P($ No prep $\mid$ first choice $)=\frac{0.190}{0.205}=93 \%$

Question 3

Which two events are most likely to be independent?

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

Answer 3

E

Question 4

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 5

Many school administrators watch enrollment numbers for answers to questions parents ask. Some parents wondered if preferring a particular science course is related to the student's preference in foreign language. Students were surveyed to establish their preference in science and foreign language courses. Does it appear that preferences in science and foreign language are independent? Explain.

Question 6

Which of these has a Geometric model?

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

Question 7

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.

$\begin{array}{|l|l|l|l|l|}\hline 10 & 30 & 10 & 30 & 10 \\\hline 20 & 10 & 50 & 10 & 20 \\\hline\end{array}$


-As you enter the store you watch the four people in front of you all win 50% discounts. The store manager tells you how lucky you are to be throwing the cube while it is on a hot streak, but the friend with you says you're unlucky because the streak can't continue. Comment on their statements.

Question 8

A survey of an introductory statistics class in Autumn 2003 asked students whether or not they ate breakfast the morning of the survey. Results are as follows:
a. What is the probability that a randomly selected student is female?
b. What is the probability that a randomly selected student ate breakfast?
c. What is the probability that a randomly selected student is a female who ate breakfast
d. What is the probability that a randomly selected student is female, given that the student
ate breakfast?
e. What is the probability that a randomly selected student ate breakfast, given that the student is female?
f. Does it appear that whether or not a student ate breakfast is independent of the student's sex? Explain.

Question 9

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

Question 10

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

Question 11

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

Question 12

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

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

Question 13

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

Question 14

We can tell that these two features are independent because...

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

Question 15

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 3 of the first 10 customers buy specialty clothes for their pet? Show work.

Question 16

Which of these random variables has a binomial model?

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

Question 17

Bowling A large corporation sponsors bowling leagues for its employees. The mean score for men was 154 pins with a standard deviation of 9 pins, while the women had mean score 144 pins and standard deviation 12 pins. At the end of the season the league holds a tournament that randomly pairs men and women as opponents in the first round.
a. On average, how much do you expect the man to win by?
b. Estimate the standard deviation of the differences in the competitor's scores. c. What assumption did you make in determining the standard deviation?

Question 18

Which of these has a Binomial model?

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

Question 19

Which of these has a geometric model?

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

Question 20

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.

-Surprised by the high number of customers who purchased magazines that day, the owner decided that his 5% estimate must have been too low. How many magazine sales would it have taken to convince you? Justify your answer.

Question 21

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 22

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.

$\begin{array}{|l|l|l|l|l|}\hline 10 & 30 & 10 & 30 & 10 \\\hline 20 & 10 & 50 & 10 & 20 \\\hline\end{array}$


-What is the probability that none of the first three customers gets more than a 30% discount?

Question 23

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 24

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 there is at least one gold winner among the first six customers?

Question 25

Ten little monkeys were jumping on a bed. There is a 35% chance that one will fall off and bump his head. In the bedroom next door, five kangaroos were jumping on a bed. Being more adept at jumping, there is only a 20% that a kangaroo will fall off the bed.

-If the monkeys enjoy this activity every night for an entire week, what are the chances that a monkey falls off the bed every one of the seven nights?

Question 26

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 27

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.

$\begin{array}{|l|l|l|l|l|}\hline\text { area} & 500 \text {sq. ft. }& 1000\text { sq. ft. }& 1500\text { sq. ft.} & 2000+ \text {sq. ft.} \\\hline \text {probability} & 0.10 & 0.25 & 0.45 & 0.20 \\\hline\end{array}$


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?

Question 28

Five multiple choice questions, each with four possible answers, appear on your history exam. What is the probability that if you just guess, you
a. get none of the questions correct?
b. get all of the questions correct?
c. get at least one of the questions wrong?
d. get your first incorrect answer on the fourth question?

Question 29

All airline passengers must pass through security screenings, but some are subjected to additional searches as well. Some travelers who carry laptops wonder if that makes them more likely to be searched. Data for 420 passengers aboard a cross-country flight are summarized in the table shown. Does it appear that being subjected to an additional search is independent of carrying a laptop computer? Explain.

Question 30

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 31

Cigarette taxes New York public health officials report that currently 22% of adults smoke (Ithaca Journal, 1/12/04). They hope that newly increased state cigarette taxes will reduce this rate. They plan to check in December by selecting a random sample of 1200 New Yorkers to estimate again the percentage of adults who smoke.
a. Verify that a Normal model is a useful approximation for the binomial in this situation. b. In that December sample, how many smokers would it take to convince you that the percentage of NY adults who smoke had decreased significantly? Explain.

Question 32

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 at least 5 of his first 50 customers buy magazines?

Question 33

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 34

Ten little monkeys were jumping on a bed. There is a 35% chance that one will fall off and bump his head. In the bedroom next door, five kangaroos were jumping on a bed. Being more adept at jumping, there is only a 20% that a kangaroo will fall off the bed.

-The monkeys manage to go a whole week without someone bumping their head. One of the kangaroos insists that they are due for an injury. Another says they must be getting better at their jumping skills. Do you think they're due for a crash?

Question 35

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 36

What are the chances that the kangaroos can jump two nights in a row with no one falling off the bed?

Question 37

Which service contract should the company expect to cost more each year? How much more? With what standard deviation?

Question 38

Verify that this scenario satisfies all four conditions for a binomial scenario.

Question 39

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 none of the first four customers gets a discount over 20%?

Question 40

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.

$\begin{array}{l|c|c|c|c|c|c} \text { E-mails received }& 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Probability} & 0.05 & 0.10 & 0.20 & 0.25 & 0.30 & 0.10\end{array}$

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 41

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 are the mean and standard deviation for the profit on a 1000 plans?

Question 42

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 43

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 44

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 45

Surprised by the high number of customers who purchased specialty pet clothing that day, the owner decided that her 4% estimate must have been too low. How many clothing sales would it have taken to convince you? Justify your answer.

Question 46

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.

-Suppose that our fearless fisherman goes out early one morning and casts a total of 250 times. What are the mean and standard deviation of the number of times he should receive a nibble on his line?

Question 47

Political analysts estimate the probability that Hillary Clinton will run for president in 2008 is 45%, and the probability that NY's Governor George Pataki will run as the Republican candidate is 20%. If their political decisions are independent, then what is the probability that only Hillary runs for president?

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

Question 48

Ten little monkeys were jumping on a bed. There is a 35% chance that one will fall off and bump his head. In the bedroom next door, five kangaroos were jumping on a bed. Being more adept at jumping, there is only a 20% that a kangaroo will fall off the bed.

-What are the chances that the kangaroos can get away with jumping on the bed for 4 straight nights until they finally have someone fall off the bed on the 5th night?

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.

-Assuming the owner is correct in thinking that 5% of the customers purchase magazines, how many customers should he expect before someone buys a magazine?

Question 50

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 51

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.

-How many times should the restaurant expect to have to get this freezer repaired over the three-year term of the lease?

Question 52

The Masterfoods company manufactures bags of Peanut Butter M&M's. They report that they make 10% each brown and red candies, and 20% each yellow, blue, and orange candies. The rest of the candies are green.
a. If you pick a Peanut Butter M&M at random, what is the probability that i. it is green?
ii. it is a primary color (red, yellow, or blue)?
iii. it is not orange?
b. If you pick four M&M's in a row, what is the probability that i. they are all blue?
ii. none are green?
iii. at least one is red?
iv. the fourth one is the first one that is brown?
c. After picking 10 M&M's in a row, you still have not picked a red one. A friend says that
you should have a better chance of getting a red candy on your next pick since you have
yet to see one. Comment on your friend's statement.

Question 53

What are the mean and standard deviation of the company's annual expense for the service contract?

Question 54

A manufacturing firm orders computer chips from three different companies: 10% from Company A; 20% from Company B; and 70% from Company C. Some of the computer chips that are ordered are defective: 4% of chips from Company A are defective; 2% of chips from Company B are defective; and 0.5% of chips from Company C are defective. A worker at the manufacturing firm discovers that a randomly selected computer chip is defective. What is the probability that the computer chip came from Company B? Show your work.

Question 55

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 56

Traffic accidents Police reports about the traffic accidents they investigated last year indicated that 40% of the accidents involved speeding, 25% involved alcohol, and 10% involved both risk factors.
a. What is the probability that an accident involved neither alcohol nor speed?
b. Do these two risk factors appear to be independent? Explain.

Question 57

Cool Off A survey of southern California houses in a given town shows that 70% of the homes have an air conditioning system and 90% of home have at least one ceiling fan. 65% of all homes surveyed had both features.
a. What is the probability that a randomly selected home neither feature?
b. What is the probability that a randomly selected home has a ceiling fan, given that it already has an air conditioning system?
c. Do these two house features appear to be independent? Justify your answer.

Question 58

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 a customer gets at least a 40% discount?

Question 59

Studying Assume that 75% of the AP* Stat students studied for this test. If 40% of those who study get an A, but only 10% of those who don't study get an A, what is the probability that someone who gets an A actually studied for the test?

Question 60

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 61

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift.

$\begin{array}{|l|l|l|l|l|}\hline \text {probability} & 0.10 & 0.25 & 0.55 & 0.10 \\\hline \text { \# of workers} & 3 & 4 & 5 & 6 \\\hline\end{array}$

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

Question 62

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

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

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

Question 68

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

Question 69

What is the probability that a randomly selected bicycle will have a kickstand or a water bottle holder?

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

Question 70

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

Question 71

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? $\begin{array}{|c|c|c|c|}\hline& \text { Lefty } & \text { Righty } & \text { Total } \\\hline \text { Boy } & & & 66 \\\hline \text { Girl } & ? & & 54 \\\hline \text { Total } & 20 & 100 & 120 \\\hline\end{array}$

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

Question 72

What is the probability that a student from this class eats breakfast but does not floss their teeth?

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

Question 73

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

Question 74

What is the probability that a student from this class eats breakfast or flosses their teeth?

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

Question 75

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

Question 76

Given that a randomly selected bike has a kickstand, what are the chances that it also has a water bottle holder?

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

Question 77

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

Question 78

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

Question 79

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? $\begin{array}{lr|c|c|c} & &{\text { Museum }} & \\& & \text { Yes } & \text { No } & \text { Total } \\\hline \text { Home } & \text { Yes } & ? ? & & 80 \\\hline \text { Depot } & \text { No } & & & 40 \\\hline & \text { Total } & 30 & 90 & 120\end{array}$

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

Question 80

What is the probability there is exactly 1 jumbo among the first 6 cones sold by the ice cream stand in #7?

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