Question 1

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?

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Question 2

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.

Accepted Answer

The answer of Cool Off A survey of southern California...

Question 3

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?

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

Question 4

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.
-Assuming the pet store owner is correct in thinking that only 4% of her customers purchase
specialty clothes for their pets, how many customers should she expect before someone
buys a garment for their pet?

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

Question 5

Still 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.
Suppose you use these two dice in a competition against another player. You will roll one
of the dice and your opponent will roll the other one. The winner is the person who rolls
the higher number. You get first choice of dice and want to win. Would you pick Die A or
Die B? Explain why.

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The answer of Still strange dice • The six faces...

Question 6

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 the tenth blood donor is the first donor with Type B blood?

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The answer of The American Red Cross says that about...

Question 7

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 8

A small business just leased a new computer and color laser printer for three years. The service contract for the computer
offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company's research
suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1%
three times, and none required more than three repairs.
-How many times should the company expect to have to get this computer repaired over
the three-year term of the lease?

Accepted Answer

The answer of A small business just leased a new...

Question 9

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.

Accepted Answer

The answer of A survey of an introductory statistics class...

Question 10

A small business just leased a new computer and color laser printer for three years. The service contract for the computer
offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company's research
suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1%
three times, and none required more than three repairs.
-Find the standard deviation of the number of repairs each year.

Accepted Answer

The answer of A small business just leased a new...

Question 11

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.
-The blood drive has a total of 150 donors. Assuming this is a typical number of donors for
a school blood drive, what would be the mean and standard deviation of the number of
donors who have Type B blood?

Accepted Answer

The answer of The American Red Cross says that about...

Question 12

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?

Accepted Answer

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

Question 13

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 at least 2 of the first 10 blood donors has Type B blood?

Accepted Answer

The answer of The American Red Cross says that about...

Question 14

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?

Accepted Answer

The answer of A new clothing store advertises that during...

Question 15

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 a monkey will not fall off the bed?

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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 18

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 19

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?

Accepted Answer

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

Question 20

What is the standard deviation of the number of repairs that may be required during the
three-year lease period? On what assumption does your calculation rest? Do you think this
assumption is reasonable? Explain.

Accepted Answer

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

Quiz 4: Randomness and Probability

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 the tenth blood donor is the first donor with Type B blood?

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 at least 2 of the first 10 blood donors has Type B blood?

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?

What is the standard deviation of the number of repairs that may be required during the three-year lease period? On what assumption does your calculation rest? Do you think this assumption is reasonable? Explain.