Question 1

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.

Accepted Answer

This is a binomial probability problem where n = 10 (number of trials), k = 7 (number of successes), and p = 0.80 (probability of success on a single trial). The formula for binomial probability is P(X = k) = (n choose k) * p^k * (1-p)^(n-k). Plugging in the values: P(X = 7) = (10 choose 7) * 0.80^7 * 0.20^3 = 0.2013.

Question 2

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.

Accepted Answer

D

Question 3

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

Accepted Answer

The probability of a given number of events in a fixed interval can be calculated using the Poisson distribution. Here, the average number of imperfections (λ) is 3, and we want the probability of 2 imperfections (k=2). The formula is P(k; λ) = (e^(-λ) * λ^k) / k!. Plugging in the values gives P(2; 3) = (e^(-3) * 3^2) / 2! = 0.2240.

Question 4

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.

Accepted Answer

The problem involves a binomial distribution, where we have a fixed number of trials (i.e. the number of luxury cars sold per month) and each trial has only two possible outcomes (i.e. silver or not silver). We are given that the probability of a luxury car being silver is 0.2.

We want to find the probability of 8 out of 20 luxury cars sold in a month being silver. Using the binomial distribution formula, we have:

P(X = 8) = (20 choose 8) * (0.2)^8 * (0.8)^12

where (20 choose 8) is the number of ways to choose 8 silver cars out of 20 (i.e. a combination). Using a calculator, we find:

(20 choose 8) = 125970

Plugging this and the given probabilities into the formula, we get:

P(X = 8) = 125970 * (0.2)^8 * (0.8)^12

P(X = 8) ≈ 0.0222

So the probability that 8 luxury cars sold in a month are silver is approximately 0.0222, or choice C.

Question 5

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.

Accepted Answer

To calculate the mean annual expense, we need to consider the probability of each scenario:
- 80% of the time, no repairs are needed. So the cost for this scenario is just the annual fee of $125. 
- 11% of the time, one repair is needed. So the cost for this scenario is the annual fee plus the repair service charge: $125 + $35 = $160
- 5% of the time, two repairs are needed. So the cost for this scenario is the annual fee plus two repair service charges: $125 + 2*$35 = $195
- 4% of the time, three repairs are needed. So the cost for this scenario is the annual fee plus three repair service charges: $125 + 3*$35 = $230

Therefore, to calculate the mean we need to multiply each scenario cost by its probability and add them up:
(0.8*$125) + (0.11*$160) + (0.05*$195) + (0.04*$230) = $122.55

Therefore, the answer is B, $122.55.

Question 6

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

Accepted Answer

The expected number of trials until the first success in a geometric distribution is given by 1/p, where p is the probability of success (in this case, finding a defective part). Given an 8% chance (or 0.08 probability) of being defective, the expected number is 1/0.08 = 12.5.

Question 7

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

Accepted Answer

It is impossible to receive more than 6 calls per hour if the distribution is uniformly between 0 and 6. Therefore, the probability is 0.

Question 8

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

Accepted Answer

The average number of imperfections for a 36 sq.ft. sheet is 3, so for an 18 sq.ft. sheet, it would be 1.5. Using the Poisson distribution with λ = 1.5, the probability of observing 2 imperfections is calculated using the formula P(X=k) = (e^(-λ) * λ^k) / k!. For k=2, this gives approximately 0.2510.

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 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.

Accepted Answer

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

Question 10

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.

Accepted Answer

The answer of Suppose that incoming calls per hour to...

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 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.

Accepted Answer

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

Question 12

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.

Accepted Answer

The expected number of new claims filed per day is 2.4, so the expected number of new claims filed per week (5 days) is:

2.4 * 5 = 12

Therefore, the answer is C.

Question 13

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.

Accepted Answer

The answer of It is estimated that 20% of luxury...

Question 14

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.

Accepted Answer

The answer of Suppose that incoming calls per hour to...

Question 15

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.

Accepted Answer

To calculate the standard deviation, we need to first find the expected value or mean number of repairs per year:

Expected value = (0.09 x 1) + (0.04 x 2) + (0.01 x 3) = 0.09 + 0.08 + 0.03 = 0.20

Next, we can calculate the variance:

Variance = (0.86 x 0^2) + (0.09 x 1^2) + (0.04 x 2^2) + (0.01 x 3^2) - 0.20^2
Variance = 0.09 + 0.32 + 0.09 - 0.04
Variance = 0.46

Finally, we take the square root of the variance to get the standard deviation:

Standard deviation = √0.46 ≈ 0.55

Therefore, the best choice is B.

Question 16

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

Accepted Answer

The answer of A specific automotive part that a service...

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 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

Accepted Answer

This is a binomial distribution problem, where n=10 (since we are looking at the 10th part retrieved) and p=0.08 (the probability of a defective part). We want the probability that the first defective part is retrieved on the 10th try, which means we have 9 non-defective parts followed by 1 defective part. The probability of this occurring is given by the binomial probability formula: 
P(X=1)= (10 choose 1) * (0.08)^1 * (0.92)^9
= 10 * 0.08 * 0.285
= 0.228

Note: This answer is very close to choice (A), but the question asks for the probability that the 10th part is the first defective, not just the overall probability that exactly one part out of ten is defective.

Question 18

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

Accepted Answer

The problem involves a Poisson distribution with an average rate (λ) of 3 imperfections per sheet. The probability of having no more than 2 imperfections is the sum of the probabilities of having 0, 1, or 2 imperfections. Calculating this using the Poisson probability formula gives approximately 0.4232.

Question 19

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

Accepted Answer

The expected number of calls resolved within one hour is calculated by multiplying the total number of calls (10) by the probability of a call being resolved within one hour (0.80), which equals 8.

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 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.

Accepted Answer

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

Quiz 8: Random Variables and Probability Models

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 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?

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?

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

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

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 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 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?