Question 1

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

Accepted Answer

The answer of BatCo, a company that sells batteries, claims...

Question 2

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.

Accepted Answer

The answer of Annual review You are up for your...

Question 3

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 black cards in a 10-card hand.
C) The number of cards drawn from a deck until we find all four aces.
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.

Accepted Answer

A geometric model is used for scenarios where we are counting the number of trials until the first success. In option E, we are counting the number of people surveyed until we find someone who owns an iPod, which fits the geometric distribution model.

Question 4

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) 80
D) 96
E) 92

Accepted Answer

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

Question 5

Grades You believe that there is a 20% chance that you will earn an A in your English
class, a 10% chance that you will earn an A in your Physics class, and a 5% chance that you
will earn an A in both classes.
a. Find the probability that you do not get an A in either English or Physics.
b. Are "earning an A in English" and "earning an A in Physics" disjoint events? Explain.
c. Are "earning an A in English" and "earning an A in Physics" independent events?
Explain.

Accepted Answer

The answer of Grades You believe that there is a...

Question 6

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

Accepted Answer

The answer of A poll of 120 Ithacans found that...

Question 7

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

Accepted Answer

Events are independent if the occurrence of one does not affect the probability of the other. Registering to vote and being left-handed are unrelated, so they are most likely independent.

Question 8

Studying Assume that 75% of the Stats 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?

Accepted Answer

The answer of Studying Assume that 75% of the Stats...

Question 9

Heights of adults According to the National Health Survey, heights of adults may have a
Normal model with mean heights of 69.1" for men and 64.0" for women. The respective
standard deviations are 2.8" and 2.5."
a. Based on this information,
i. how much taller are men than women, on average?
ii. what is the standard deviation for the difference in men's and women's heights?
b. Assume that women date men without considering the height of the man (i.e., that the
heights of the couple are independent). What is the probability that a woman dates a man
shorter than she is?

Accepted Answer

The answer of Heights of adults According to the National...

Question 10

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

Accepted Answer

A binomial model is appropriate for situations with a fixed number of independent trials, each with two possible outcomes (success or failure). In option B, each at-bat is an independent trial with two outcomes: hit or no hit.

Question 11

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

Accepted Answer

The probability of finding two free bottles in a 6-pack follows a binomial distribution with n = 6 trials and p = 0.12 probability of success. The probability is calculated using the binomial probability formula: P(X = 2) = C(6,2) * (0.12)^2 * (0.88)^4 ≈ 0.13 or 13%.

Question 12

Home ownership According to the Bureau of the Census, 68.0% of Americans owned their
own homes in 2003. A local real estate office is curious as to whether a higher percentage of
Americans own their own homes in its area. The office selects a random sample of 200
people in the area to estimate the percentage of those people that own their own homes.
a. Verify that a Normal model is a useful approximation for the Binomial in this situation.
b. What is the probability that at least 140 people will report owning their own home?
c. Based on the sample, how many people would it take for you to be convinced that a
higher percentage of Americans own their own homes in that area? Explain.

Accepted Answer

The answer of Home ownership According to the Bureau of...

Question 13

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?

Accepted Answer

The answer of Passing the test Assume that 70% of...

Question 14

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

Accepted Answer

The answer of A national study found that the average...

Question 15

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

Accepted Answer

The geometric model is used to find the probability of the first success on the nth trial in a series of independent Bernoulli trials. Option E fits this model as it involves surveying people until the first success (finding someone who has taken Statistics).

Question 16

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

Accepted Answer

The probability of being ticketed for speeding but not for running a red light is 12% - 4% = 8%.

Question 17

Luxury cars According to infoplease, 18.8% of the luxury cars manufactured in 2003 were
silver. A large car dealership typically sells 50 luxury cars a month.
a. Explain why you think that the luxury car sales can be considered Bernoulli trials.
b. What is the probability that the fifth luxury car sold is the first silver one?
c. Let X represent the number of silver luxury cars sold in a typical month. What is the
probability model for X? Specify the model (name and parameters), and tell the mean and
standard deviation.

Accepted Answer

The answer of Luxury cars According to infoplease, 18.8% of...

Question 18

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 $$92 + 96 = 188$$
8 minutes. What
Is the standard deviation of
Their total time?
A) 20 minutes
B) 6 minutes
C) 4.5 minutes
D) It cannot be determined.
E) 2 minutes

Accepted Answer

The answer of Some marathons allow two runners to "split"...

Question 19

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) 2
D) 99.8
E) 200

Accepted Answer

The answer of A supermarket claims that their checkout scanners...

Question 20

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? 
A) $\frac { 42 } { 90 }$
B) $\frac { 52 } { 100 }$
C) $\frac { 52 } { 90 }$
D) $\frac { 42 } { 100 }$
E) $\frac { 66 } { 90 }$

Accepted Answer

The answer of Six Republicans and four Democrats have applied...

Quiz 8: Regression, Associations, and Predictive Modeling

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?

Which of these has a geometric model?

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 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?

Which two events are most likely to be independent?

Studying Assume that 75% of the Stats 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?

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

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?

Which of these has a Geometric model?

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 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?

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?