Question 1

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 1 $$18 + 34 = 52$$
Points. What is the standard deviation of their combined
Scores?
A) 15
B) 137
C) cannot be determined
D) 11.7
E) 5.3

Accepted Answer

The answer of On a physical fitness test middle school...

Question 2

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?

Accepted Answer

The answer of Basketball player heights Assume the heights of...

Question 3

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

Accepted Answer

A geometric model is used for the number of trials until the first success in a series of independent Bernoulli trials. Option A fits this description as it involves counting the number of people checked until finding the first person with green eyes.

Question 4

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?

Accepted Answer

The answer of Bowling A large corporation sponsors bowling leagues...

Question 5

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

Accepted Answer

The answer of The city council has 6 men and...

Question 6

Credit card sales The National Association of Retailers reports that 62% of all purchases
are now made by credit card; you think this is true at your store as well. On a typical day
you make 20 sales.
a. Explain why your sales can be considered Bernoulli trials.
b. What is the probability that your fourth customer is the first one who uses a credit card?
c. Let X represent the number of customers who use a credit card on a typical day. What is
the probability model for X? Specify the model (name and parameters), and tell the mean
and standard deviation.
d. What is the probability that on a typical day at least half of your customers use a credit
card?

Accepted Answer

The answer of Credit card sales The National Association of...

Question 7

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

Accepted Answer

The answer of A friend of yours plans to toss...

Question 8

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.

Accepted Answer

The answer of Traffic accidents Police reports about the traffic...

Question 9

Which two events are most likely to be independent?
A) having a car accident, and having 3 inches of snow today
B) having a driver's license, and having blue eyes
C) having a flat tire, and being late for school
D) being a senior, and leaving campus for lunch
E) getting an A in math, and getting an A in Physics

Accepted Answer

Having a driver's license and having blue eyes are most likely independent because possessing a driver's license is unrelated to a person's eye color.

Question 10

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.

Accepted Answer

The answer of Cigarette taxes New York public health officials...

Question 11

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.

Accepted Answer

The answer of Seatbelts Safety officials hope a public information...

Question 12

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?

Accepted Answer

The answer of SAT prep Surveys indicate that 5% of...

Question 13

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) 60%
C) 33%
D) 40%
E) 8%

Accepted Answer

The probability that the first jumbo cone is the fourth cone sold follows a geometric distribution with p = 0.12. The probability is (0.88)^3 * 0.12 = 0.072, which is approximately 8%.

Question 14

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 Democrats among a group of 20 randomly chosen adults.
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.

Accepted Answer

A binomial model is appropriate when there are a fixed number of independent trials, each with two possible outcomes. Choice B fits this as it involves a fixed number of trials (20 adults) with two outcomes (Democrat or not).

Question 15

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

Accepted Answer

The answer of A survey of some AP* Stats students...

Question 16

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

Accepted Answer

The probability of exactly 1 jumbo cone in 6 sales can be calculated using the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n=6, k=1, and p=0.12. This results in approximately 38%.

Question 17

Smoking State public health officials claim that 18% of adults currently smoke cigarettes.
a. We start selecting a few adults at random, asking each if he or she is a smoker. Explain
why these can be considered Bernoulli trials.
b. How many people do you expect to have to ask in order to find a smoker?
c. Let X represent the number of smokers among a randomly chosen sample of 30 adults.
What is the probability model for X? Name the model (including its parameters) and
specify the mean and standard deviation of X.
d. What is the probability that there are at least 8 smokers among our sample of 30 people?

Accepted Answer

The answer of Smoking State public health officials claim that...

Question 18

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.

Accepted Answer

The answer of Strange dice A game is played with...

Question 19

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

Accepted Answer

The probability that only Candidate A runs is the probability that A runs and B does not run. This is calculated as 0.45 * (1 - 0.20) = 0.45 * 0.80 = 0.36 or 36%.

Question 20

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.

Accepted Answer

The answer of Dice rolls Two players compete against each...

Quiz 8: Regression, Associations, and Predictive Modeling

Which of these random variables has a geometric model?

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 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?

Which two events are most likely to be independent?

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?

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

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?

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?

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.

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?