Question 1

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.

Accepted Answer

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Question 2

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 if the monkeys jump every day for a week that at least one will
fall off of the bed?

Accepted Answer

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Question 3

For purposes of making budget plans for staffing, a college reviewed student's year in
school and area of study. Of the students, 22.5% are seniors, 25% are juniors, 25% are
sophomores, and the rest are freshmen. Also, 40% of the seniors major in the area of
humanities, as did 39% of the juniors, 40% of the sophomores, and 36% of the freshmen.
What is the probability that a randomly selected humanities major is a junior? Show your
work.

Accepted Answer

The answer of For purposes of making budget plans for...

Question 4

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

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Question 5

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

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Question 6

What is the probability that none of the first four customers gets a discount over 20%?

Accepted Answer

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Question 7

Five

Accepted Answer

The answer of Five...

Question 8

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.
-Find the standard deviation of the number of repairs each year.

Accepted Answer

The answer of A fast food restaurant just leased a...

Question 9

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 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

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

Accepted Answer

The answer of A fast food restaurant just leased a...

Question 12

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 13

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 14

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 a 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.

Accepted Answer

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

Question 15

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 he will cast his line without success 20 times before finally
succeeding the 21st time?

Accepted Answer

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

Question 16

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 17

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 a customer gets more than a 20% discount?

Accepted Answer

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

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 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?

Accepted Answer

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

Question 20

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.
-The service contract for the printer estimates a mean annual cost of $120 with standard
deviation of $30. What is the expected value and standard deviation of the total cost for the
service contracts on computer and printer?

Accepted Answer

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

Quiz 4: Randomness and Probability

What is the probability that none of the first four customers gets a discount over 20%?

Five

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?