Question 1

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 2

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.
-What is the probability that the fisherman will get 5 nibbles on his line.

Accepted Answer

The answer of A young boy is fishing off the...

Question 3

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?

Accepted Answer

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

Question 4

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?

Accepted Answer

The answer of A sporting goods store announces a "Wheel...

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.

Accepted Answer

The answer of Many school administrators watch enrollment numbers for...

Question 6

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?

Accepted Answer

The answer of The owner of a small convenience store...

Question 7

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?

Accepted Answer

The answer of Jacob has a bag of his favorite...

Question 8

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 9

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.

Accepted Answer

The answer of The Masterfoods company manufactures bags of Peanut...

Question 10

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.

Accepted Answer

The answer of A survey of local car dealers revealed...

Question 11

Surprised by a 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.

Accepted Answer

The answer of Surprised by a high number of customers...

Question 12

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?

Accepted Answer

The answer of Ten little monkeys were jumping on a...

Question 13

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?

Accepted Answer

The answer of A cell phone company offers a simple...

Question 14

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

Accepted Answer

The answer of The owner of a pet store is...

Question 15

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.

Accepted Answer

The answer of The owner of a pet store is...

Question 16

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...

Question 17

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?

Accepted Answer

The answer of The owner of a small convenience store...

Question 18

What is the standard deviation of the 10 total warranty plans? What assumption does this
calculation require? Do you think this assumption is reasonable?

Accepted Answer

The answer of What is the standard deviation of the...

Question 19

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?

Accepted Answer

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

Question 20

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?

Accepted Answer

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

Exam 4: Randomness and Probability

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?

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?

Surprised by a 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.

What is the standard deviation of the 10 total warranty plans? What assumption does this calculation require? Do you think this assumption is reasonable?

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 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?