Deck 6: Random Variables and Probability Models

Question 1

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 1

12

Question 2

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 2

0.0222

Question 3

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

Answer 3

0.0378

Question 4

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 5

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 6

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 7

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 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 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 9

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 10

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 11

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 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.
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 13

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 14

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 15

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 16

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

Question 17

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 18

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 19

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 20

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.