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 of1000 sim chips has 2 imperfections?
A) 0.2240
B) 0.4232
C) 0.2510
D) 0.4591
E) 0.1365

Accepted Answer

The scenario described follows a Poisson distribution, where the average number of imperfections per 1000 sim chips is 3. The probability of finding exactly 2 imperfections in a sample of 1000 sim chips can be calculated using the Poisson probability formula: P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average number of successes (3 in this case), k is the number of successes we're interested in (2), and e is the base of the natural logarithm. Plugging in the values gives us the probability for 2 imperfections, which matches choice A, 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.

Accepted Answer

To calculate the mean annual expense with the service contract for the freezer, we consider the probabilities and costs associated with each repair scenario. The service contract costs $125 annually, plus a $35 service charge for each repair. The expected number of repairs and their associated costs are as follows:- 80% of the time, no repairs are needed, so the cost is $125.- 11% of the time, one repair is needed, so the cost is $125 + $35 = $160.- 5% of the time, two repairs are needed, so the cost is $125 + $35*2 = $195.- 4% of the time, three repairs are needed, so the cost is $125 + $35*3 = $230.The mean annual expense is calculated by multiplying each scenario's cost by its probability and summing these products:$$ \text{Mean Expense} = 0.80(125) + 0.11(160) + 0.05(195) + 0.04(230) $$$$ = 100 + 17.6 + 9.75 + 9.2 $$$$ = 136.55 $$Therefore, the correct answer is $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.

Accepted Answer

The number of successes (silver cars sold) follows a binomial distribution with parameters n = 20 (number of trials per month) and p = 0.2 (probability that a car is silver). We want to find the probability of getting exactly 8 silver cars sold in a month, so we use the binomial probability formula:
P(X = 8) = (20 choose 8) * 0.2^8 * (1 - 0.2)^12
= 125970 * 0.004096 * 0.068719
= 0.0222 (approximately)

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

Accepted Answer

The probability that the fourth part is the first defective one follows a geometric distribution with p = 0.08. The probability is calculated as (0.92)^3 * 0.08 = 0.0623.

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.

Accepted Answer

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

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.

Accepted Answer

The standard deviation is the square root of the variance. The variance is the expected value of the squared deviation from the mean. The mean number of repairs is 0.8 * 0 + 0.11 * 1 + 0.05 * 2 + 0.04 * 3 = 0.19 repairs. The variance is 0.8 * (0 - 0.19)^2 + 0.11 * (1 - 0.19)^2 + 0.05 * (2 - 0.19)^2 + 0.04 * (3 - 0.19)^2 = 0.512 repairs^2. The standard deviation is the square root of 0.512 repairs^2, which is 0.72 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.

Accepted Answer

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

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?

Accepted Answer

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

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?

Accepted Answer

The answer of For quality control purposes, a company that...

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?

Accepted Answer

The answer of Internet service providers (ISP) need to resolve...

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?

Accepted Answer

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

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?

Accepted Answer

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

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: $$\begin{array} { | c | c | } 
\hline \text { Number of Claims } & \text { Probability } \
\hline 0 & .05 \
\hline 1 & .15 \
\hline 2 & .25 \
\hline 3 & .45 \
\hline 4 & .10 \
\hline
\end{array}$$ 
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.

Accepted Answer

The answer of A local unemployment office keeps track of...

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

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 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?

Accepted Answer

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

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.

Accepted Answer

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

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

Accepted Answer

It is impossible to receive more than 6 calls per hour if the incoming calls per hour are uniformly distributed between 0 and 6. Therefore, the probability of receiving more than 6 calls is 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?

Accepted Answer

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

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.

Accepted Answer

The expected value of the number of repairs can be calculated as follows:
E(X) = (0.86 x 0) + (0.09 x 1) + (0.04 x 2) + (0.01 x 3) = 0.22
The variance can be calculated as follows:
Var(X) = (0.86 x (0-0.22)^2) + (0.09 x (1-0.22)^2) + (0.04 x (2-0.22)^2) + (0.01 x (3-0.22)^2) = 0.3536
The standard deviation is the square root of the variance:
SD = sqrt(0.3536) = 0.5943 ≈ 0.55
Therefore, the best choice is B.

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.

Accepted Answer

The expected number of repairs is 0.20 repairs per year. This is calculated by multiplying the probability of each number of repairs by the number of repairs, and then adding the results together. For example, the probability of needing no repairs is 0.86, and the number of repairs is 0, so the expected number of repairs for this outcome is 0.86 * 0 = 0. The probability of needing one repair is 0.09, and the number of repairs is 1, so the expected number of repairs for this outcome is 0.09 * 1 = 0.09. The probability of needing two repairs is 0.04, and the number of repairs is 2, so the expected number of repairs for this outcome is 0.04 * 2 = 0.08. The probability of needing three repairs is 0.01, and the number of repairs is 3, so the expected number of repairs for this outcome is 0.01 * 3 = 0.03. Adding these results together gives us 0 + 0.09 + 0.08 + 0.03 = 0.20.

Quiz 6: Random Variables and Probability Models

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 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?

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 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. The probability that fewer than 3 Calls are received per hour 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. What is the probability that more Than 6 calls are received per hour?