Deck 6: Random Variables and Probability Models

Question 1

For quality control purposes, a company that manufactures sim chips for cell/smart phones routinely takes samples from its production process. Since it is important that
These chips are nearly fault free, one inspection check involves using microscopic
Equipment to count the number of imperfections on each chip. Suppose the average
Number of imperfections per 1000 sim chips is 3. What is the probability that a sample of
1000 sim chips has 2 imperfections?

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

Answer 1

0.2240

Question 2

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.

Answer 2

$136.55.

Question 3

It is estimated that 20% of luxury cars manufactured in 2012 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) 0.0006.
B) 0.1276.
C) 0.0222.
D) 0.7779.
E) None of the above.

Answer 3

0.0222.

Question 4

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 5

It is estimated that 20% of luxury cars manufactured in 2012 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) 0.0006.
B) 0.1276.
C) 0.0222.
D) 0.7779.
E) None of the above.

Question 6

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) 0.512 repairs2.
C) 1.25 repairs.
D) 2.5 repairs2.
E) 0.33 repairs.

Question 7

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 8

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 9

For quality control purposes, a company that manufactures sim chips for cell/smart
phones routinely takes samples from its production process. Since it is important that
these chips are nearly fault free, one inspection check involves using microscopic
equipment to count the number of imperfections on each chip. Suppose the average
number of imperfections per 1000 sim chips is 3.
A. What is the probability that a sheet of this size has 2 imperfections?
b. What is the probability that a sheet of this size has no more than 2 imperfections?
c. What is the probability that a sheet half this size (18 sq. ft.) has 2 imperfections?

Question 10

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 11

It is estimated that 20% of luxury cars manufactured in 2012 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 12

A small business just leased a new presentation equipment and a 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

A local unemployment office keeps track of the number of new claims filed each day.
Based on the data collected, it determines that the following probability distribution
applies:
A. What is the expected number of new claims filed each day?
b. What is the standard deviation in the number of new claims filed each day?
c. What is the expected number of new claims filed each week? Assume the
unemployment office is open 5 days a week.
d. What is the standard deviation in the number of new claims filed each week? Assume
the unemployment office is open 5 days a week.

Question 14

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 15

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.
A. Find the expected number of repairs for this freezer per year.
b. Find the standard deviation of the number of repairs per year.
c. What are the mean and standard deviation of the restaurant's annual expense with the
service contract for the freezer?

Question 16

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 17

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 18

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.
A. What is the probability that the fourth part retrieved from stock is the first defective?
b. What is the probability that the tenth part retrieved from stock is defective?
c. What is the expected number of parts retrieved until the first defective part?

Question 19

A small business just leased a new presentation equipment and a 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 20

A small business just leased a new presentation equipment and a 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.
Find the expected number of repairs for this kind of computer per year.

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

Question 21

A small business just leased a new presentation equipment and a 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
Presentation equipment is

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

Question 22

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.

Question 23

For quality control purposes, a company that manufactures sim chips for cell/smart phones routinely takes samples from its production process. Since it is important that
These chips are nearly fault free, one inspection check involves using microscopic
Equipment to count the number of imperfections on each chip. Suppose the average
Number of imperfections per 1000 sim chips is 3.What is the probability that a sample 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 24

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 25

For quality control purposes, a company that manufactures sim chips for cell/smart phones routinely takes samples from its production process. Since it is important that
These chips are nearly fault free, one inspection check involves using microscopic
Equipment to count the number of imperfections on each chip. Suppose the average
Number of imperfections per 1000 sim chips is 3. What is the probability that a sample
This size (1000 chips) has 2 imperfections?

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

Question 26

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 27

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.

Question 28

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