Deck 8: Random Variables and Probability Models

Question 1

Solve applications involving expected values.
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 indicates that
During a given year 86% of these computers need no repairs, 9% need to be repaired
Once, 4% twice, 1% three times, and none required more than three repairs. The standard
Deviation of the company's annual expense with the service contract for the computer is

A) $105.
B) $10.25.
C) $187.42.
D) $13.69.
E) $2.75.

Answer 1

D

Question 2

Solve applications involving expected values.
A local unemployment office keeps track of the number of new claims filed each day.
Based on data collected, it determines that the expected number of new claims filed per
Day is 2.4 with a standard deviation of 0.8688. Suppose that the office is open five days
Per week. The expected number of new claims filed per week at this office is

A) 7.4.
B) 4.344.
C) 12.
D) 10.
E) 5.25.

Answer 2

C

Question 3

Find the expected value and standard deviation of a random variable.
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 indicates that
During a given year 86% of these computers need no repairs, 9% need to be repaired
Once, 4% twice, 1% three times, and none required more than three repairs. The expected
Number of repairs for this kind of computer per year is

A) 0.20 repairs.
B) 0.55 repairs.
C) 0.89 repairs.
D) 1.00 repairs.
E) 1.20 repairs.

Answer 3

A

Question 4

Find the expected value and standard deviation of a random variable.

-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 indicates 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. The standard deviation
Of the number of repairs for this freezer per year is

A) 0.72 repairs.
B) $\text { B. } 0.512 \text { repairs } { } ^ { 2 } \text {. }$
C)C 1.25 repairs.
D) 2.5 repairs2.
E) 0.33 repairs.

Question 5

Use the appropriate probability model (Geometric).
A specific automotive part that a service station stocks in its inventory has an 8%
Chance of being defective. Suppose many cars come into the service station needing this
Part each week. What is the probability that the fourth part retrieved from stock is the
First defective?

A) 0.0064
B) 0.08
C) 0.0378
D) 0.0623
E) 0.3244

Question 6

It is estimated that 20% of luxury cars manufactured in 2008 were silver. A car
dealership typically sells 20 luxury cars per month.
a. What is the probability that 8 of the luxury cars sold per month are silver?
b. What is the probability that more than 10 of the luxury cars sold per month are silver?
c. How many silver luxury cars would you expect are sold per month?

Question 7

Find the expected value and standard deviation of a random variable.
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 indicates that
During a given year 86% of these computers need no repairs, 9% need to be repaired
Once, 4% twice, 1% three times, and none required more than three repairs. The standard
Deviation in the number of repairs for this kind of computer per year is

A) 0.20 repairs.
B) 0.55 repairs.
C) 0.89 repairs.
D) 1.00 repairs.
E) 1.20 repairs.

Question 8

Use the appropriate probability model (Binomial).
It is estimated that 20% of luxury cars manufactured in 2008 were silver. A car
Dealership typically sells 20 luxury cars per month. The probability that more than 10 of
The luxury cars sold per month are silver is

A) .0006.
B) .1276.
C) .0222.
D) .7779
E) None of the above.

Question 9

Suppose that incoming calls per hour to a customer service center of a small credit
union are uniformly distributed between 0 and 6 calls.
a. What is the probability that fewer than 3 calls are received per hour?
b. What is the probability that at least 3 calls are received per hour?
c. What is the probability that more than 6 calls are received per hour?

Question 10

Use the appropriate probability model (Uniform).
Suppose that incoming calls per hour to a customer service center of a small credit
Union are uniformly distributed between 0 and 6 calls. What is the probability that more
Than 6 calls are received per hour?

A) 1 / 6
B) 1 / 7
C) 1
D) 3 / 7
E) 0

Question 11

Solve applications involving expected values.
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 indicates 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. The mean restaurant's
Annual expense with the service contract for this freezer is

A) $25.20.
B) $136.55.
C) $122.45.
D) $89.90.
E) $0.

Question 12

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 indicates that
during a given year 86% of these computers need no repairs, 9% need to be repaired
once, 4% twice, 1% three times, and none required more than three repairs.
a. Find the expected number of repairs for this kind of computer per year.
b. Find the standard deviation of the number of repairs per year.
c. What are the mean and standard deviation of the company's annual expense with the service contract for the computer?

Question 13

Use the appropriate probability model (Geometric).
A specific automotive part that a service station stocks in its inventory has an 8%
Chance of being defective. Suppose many cars come into the service station needing this
Part each week. What is the expected number of parts retrieved until the first defective?

A) 8
B) 12.5
C) 10.5
D) 15
E) 20

Question 14

Use the appropriate probability model (Binomial).
Internet service providers (ISP) need to resolve customer problems as quickly as
Possible. For one ISP, past data indicates that the likelihood is .80 that customer calls
Regarding Internet service interruptions are resolved within one hour. Out of the next 10
Customer calls about interrupted service, how many would be expected to have their
Service problems resolved within one hour?

A) 2
B) 4
C) 6
D) 8
E) 10

Question 15

Use the appropriate probability model (Binomial).
Internet service providers (ISP) need to resolve customer problems as quickly as
Possible. For one ISP, past data indicates that the likelihood is .80 that customer calls
Regarding Internet service interruptions are resolved within one hour. Out of the next 10
Customer calls about interrupted service, the probability that exactly 7 will be resolved
Within one hour is

A) 0.2013.
B) 0.8791.
C) 0.7897.
D) 0.3452.
E) 0.1209.

Question 16

Use the appropriate probability model (Binomial).
It is estimated that 20% of luxury cars manufactured in 2008 were silver. A car
Dealership typically sells 20 luxury cars per month. The probability that 8 of the luxury
Cars sold per month are silver is

A) .0006.
B) .1276.
C) .0222.
D) .7779
E) None of the above.

Question 17

Use the appropriate probability model (Poisson).
For quality control purposes, a company that manufactures copper sheets routinely
Takes samples from its production process. Since its product is often used for decorative
Purposes, one inspection check involves counting the number of imperfections or flaws
On sheets that measure 36 sq. ft. Suppose the average number of imperfections per sheet
Of this size is 3. What is the probability that a sheet of this size has 2 imperfections?

A) 0.2240
B) 0.4232
C) 0.2510
D) 0.4591
E) 0.1365

Question 18

Find the expected value and standard deviation of a random variable.
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 indicates 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. The expected number
Of repairs for this freezer per year is

A) 1 repair.
B) 1.25 repairs.
C) 0.33 repairs.
D) 0.79 repairs.
E) 2.5 repairs.

Question 19

Internet service providers (ISP) need to resolve customer problems as quickly as
possible. For one ISP, past data indicate that the likelihood is .80 that customer calls
regarding Internet service interruptions are resolved within one hour. Out of the next 10
customer calls about interrupted service,
a. What is the probability that exactly 7 will be resolved within one hour?
b. What is the probability that at least 7 will be resolved within one hour?
c. How many customers would be expected to have their service problems resolved
within one hour?

Question 20

Use the appropriate probability model (Uniform).
Suppose that incoming calls per hour to a customer service center of a small credit
Union are uniformly distributed between 0 and 6 calls. The probability that fewer than 3
Calls are received per hour is

A) 3 / 6.
B) 4 / 6.
C) 3 / 7.
D) 4 / 7.
E) 1 / 6.

Question 21

Use the appropriate probability model (Poisson).
For quality control purposes, a company that manufactures copper sheets routinely
Takes samples from its production process. Since its product is often used for decorative
Purposes, one inspection check involves counting the number of imperfections or flaws
On sheets that measure 36 sq. ft. Suppose the average number of imperfections per sheet
Of this size is 3. What is the probability that a sheet of this size has no more than 2
Imperfections?

A) 0.4232
B) 0.2510
C) 0.2240
D) 0.5689
E) 0.0034

Question 22

Use the appropriate probability model (Poisson).
For quality control purposes, a company that manufactures copper sheets routinely
Takes samples from its production process. Since its product is often used for decorative
Purposes, one inspection check involves counting the number of imperfections or flaws
On sheets that measure 36 sq. ft. Suppose the average number of imperfections per sheet
Of this size is 3. What is the probability that a sheet half this size (18 sq. ft.) has 2
Imperfections?

A) 0.4232
B) 0.2510
C) 0.2240
D) 0.5689
E) 0.0034

Question 23

Use the appropriate probability model (Geometric).
A specific automotive part that a service station stocks in its inventory has an 8%
Chance of being defective. Suppose many cars come into the service station needing this
Part each week. What is the probability that the tenth part retrieved from stock is the
First defective?

A) 0.2348
B) 0.4344
C) 0.0378
D) 0.4722
E) 0.3780

Question 24

Use the appropriate probability model (Uniform).
Suppose that incoming calls per hour to a customer service center of a small credit
Union are uniformly distributed between 0 and 6 calls. The probability that at least 3 calls
Are received per hour is

A) 3 / 6.
B) 4 / 7.
C) 3 / 7.
D) 4 / 6.
E) 1 / 6.