Disc3_Soln
pdf
keyboard_arrow_up
School
University of Wisconsin, Madison *
*We aren’t endorsed by this school
Course
324
Subject
Mechanical Engineering
Date
Dec 6, 2023
Type
Pages
3
Uploaded by CoachFog15516
Discussion 3 Solutions
Warmup
Discuss the Week 3 Quiz Question number 3 with the classmates around you.
Relationship between two variables within a single group
Exercise 1
Reconsider the engineering graduates data set in Engineering_Undergraduates_sample_1000.csv
from discussion 2. It contains information on 1000 engineering graduates from two schools, Regional Technical
Institute and the State Polytechnic. We will be concerned with whether a graduate graduated with honors
(GPA>3.5) and which school they attended.
Optionally run the code below to generate the contingency table relating school and high honors status
(change eval=TRUE).
#read in Engineering_Undergraduates_sample_1000.csv after saving .csv and .Rmd in same folder
engineers
=
read.csv
(
"Engineering_Undergraduates_sample_1000.csv"
,
header=
TRUE
)
#resave honors and school as categorical vectors in the engineers data frame.
engineers
$
honors
=
as.factor
(engineers
$
GPA
>
3.5
)
engineers
$
School
=
as.factor
(engineers
$
School)
#This will rename the factor levels to be more descriptive
levels
(engineers
$
honors)
=
c
(
"no.honors"
,
"honors"
)
#the table() function and R will make a contingency table for us from the two variables we care about
addmargins
(
table
(engineers
$
School, engineers
$
honors))
no honors
yes honors
Total
RTI
342
155
497
State Poly
294
209
503
Total
636
364
1000
a.
If we were to choose one of the graduates at random from these 1000, what is the probability
that the engineer graduated with honors?
ANSWER:
364
1000
= 0
.
364
b.
If we were to choose three engineers at random from these 1000 (without replacement), what
is the probability that all three graduated with honors?
ANSWER:
364
1000
∗
363
999
∗
362
998
= 0
.
04797561
Note: this computation is doing:
P
(
H
1
AND H
2
AND H
3) =
P
(
H
1)
∗
P
(
H
2
|
H
1)
∗
P
(
H
3
|
(
H
1
AND H
2))
where
P(1st student honors)=364/1000
P(2nd student Honors | 1st student honors)=363/999
P(3rd student Honors | (1st student AND 2nd student honors)=362/998
1
364
*
363
*
362
/
(
1000
*
999
*
998
)
#=0.04797561
## [1] 0.04797561
c.
If we choose one of the engineers who graduated with honors at random to evaluate further,
what is the probability that they attended RTI?
ANSWER:
P
(
RTI
|
Honors
) =
P
(
RT IandHonors
)
P
(
Honors
)
=
155
/
1000
364
/
1000
=
155
364
= 0
.
4258242
d.
To what quantity should you compare the value from part (c) to see if there is a mathematical
independence between honors and school in this group of 1000 observations?
Do this
comparison and draw a conclusion.
Answer: If
P
(
RTI
|
Honors
) =
P
(
RTI
)
, then the events RTI and Honors are independent in the
set of data. The overall probability of having attended RTI in this group
P
(
RTI
) =
497
1000
= 0
.
497
is higher than the probability of having attended RTI among those engineers with honors.
There is not an independence in this group of 1000 observations.
Exercise 2
A hospital has three emergency generators for use in case of a power failure. Each generator
operates independently and the manufacturer claims that the probability each generator will function properly
during a power failure is 0.95.
a.
Complete the table below by calculating the probability that 0, 1, 2, or 3 of the emergency
generators will
fail
during the next power outage.
Solve using regular probability ideas since they will not have learned about binomial yet (help
them think about P(x=0) means all 3 did not fail, so we would need to multiply 0.05 by itself
3 times). Etc.
Number of Failures
P(X=x)
0
1
∗
(
.
05)
0
∗
(0
.
95)
3
= 0
.
857375
1
3
∗
(
.
05)
1
∗
(0
.
95)
2
= 0
.
135375
2
3
∗
(
.
05)
2
∗
(0
.
95)
1
= 0
.
007125
3
1
∗
(
.
05)
3
∗
(0
.
95)
0
= 0
.
000125
b.
Suppose a power failure occurs. What is the probability that at least one generator keeps
working?
P(at least one generator keeps working)=P(0, 1, or 2 fail)=1-P(3 fails)=1-0.000125=0.999875
c.
Explain (briefly) how you can use the following simulation to check your answer for parts a
and b. Some questions to consider: Why did I define WillFail as I did? What values are
stored into the CountFailed vector? What does the histogram show?
WillFail is a vector that is 5% 1’s and 95% 0s- since we had a 0.05 prob of failure and 0.95
prob of not failure failure. The variable samp is a sample of 3 generators (we observe either
0 or 1), so sum(samp) will have the values: 0, 1, 2, 3. The sum(samp) values get stored in
CountFailed. Countfailed is a vector saving off how many of the 3 generators failed in each of
the 100000 samples of size 3. So we can use the relative frequency of each value (0-3) to check
prob. computed in a. Eg: 85695/100000= 0.85695 in 85695 of the 100000 samples of size 3,
none (0) of the generators failed.
WillFail
=
c
(
rep
(
1
,
5
),
rep
(
0
,
95
))
manytimes
=
100000
CountFailed
=
rep
(
0
,manytimes)
set.seed
(
1
)
for
(i
in
1
:
manytimes){
2
samp
=
sample
(WillFail,
3
,
replace=
TRUE
)
CountFailed[i]
=
sum
(samp)
}
hist
(CountFailed,
labels=
TRUE
,
ylim=
c
(
0
,.
95
*
manytimes),
breaks=
seq
(
-
0.5
,
3.5
,
1
))
Histogram of CountFailed
CountFailed
Frequency
0
1
2
3
0
20000
60000
85695
13617
679
9
#emperical check of part (b)
sum
(CountFailed
<
3
)
/
manytimes
## [1] 0.99991
1
-
sum
(CountFailed
==
3
)
/
manytimes
## [1] 0.99991
3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Documents
Related Questions
Two sport utility vehicles (SUVs) are being considered by a recent engineering graduate. Using the following data evaluate which sport utility vehicle is better. Use six attributes in your a
point, overall appearance, comfort, safety, reliability, and fuel mileage. Larger scores on overall appearance, comfort, safety, reliability, and fuel mileage are preferred to smaller ones.
Click the icon to view the table with data you have gathered about the SUVs.
Determine attribute weights and use the nondimensional scaling technique to find the resulting set of vehicle scores. Fill in the table below. (Round to two decimal places.)
More Info
Attribute
Price
Appearance
Comfort
Safety
Reliability
Fuel mileage
Relative
Rank
4
253 6
1
Print
Final score
Alternatives
SUV 1
$27,650
4
3
3
3
22 mpg
SUV 1
Done
Alternatives
SUV 2
$21,900
3
5
4
4
18 mpg
SUV 2
-
X
arrow_forward
Cathy Gwynn for a class project is analyzing a "Quick Shop" grocery store. The store emphasizes quick service, a limited assortment of grocery items, and higher prices. Cathy wants to see if the store hours (currently 0600 to 0100) can be changed to make the store more profitable.
Time Period
Daily Sales in the Time Period
0600-0700
$40
0700-0800
70
0800-0900
120
0900-1200
400
1200-1500
450
1500-1800
500
1800-2000
600
2000-2200
200
2200-2300
50
2300-2400
85
2400-0100
40
The cost ofthe groceries sold averages 65% of sales. The incremental cost to keep the store open, including the clerk's wage and other operating costs, is S23 per hour. To maximize profit, when should the store be opened, and when should it be closed?
arrow_forward
This question about Sanitary Engineering
Note: please solve the question using Incremental Increase Method.
arrow_forward
Projects A and B are mutually exclusive. The minimum attractive rate of return (MARR) is 12%.
Using rate of return analysis, which project should be selected?
If the image fails to load here, go to https://www.dropbox.com/s/ld6wctqieu8jgwp/ROR.jpg
Year
0
1
2
3
4
ROR
A
- $750
$200
$200
$200
$600
17.68%
B
- $1,150
$300
$350
$400
$700
16.44%
O Project A
O Project B
O Both Project A and B
O Select none of the project.
O Insufficient information to make a decision.
B-A
- $400
$100
$150
$200
$100
13.69%
arrow_forward
You are a biomedical engineer working for a small orthopaedic firm that fabricates rectangular shaped fracture
fixation plates from titanium alloy (model = "Ti Fix-It") materials. A recent clinical report documents some problems with the plates
implanted into fractured limbs. Specifically, some plates have become permanently bent while patients are in rehab and doing partial
weight bearing activities.
Your boss asks you to review the technical report that was generated by the previous test engineer (whose job you now have!) and used to
verify the design. The brief report states the following... "Ti Fix-It plates were manufactured from Ti-6Al-4V (grade 5) and machined into
solid 150 mm long beams with a 4 mm thick and 15 mm wide cross section. Each Ti Fix-It plate was loaded in equilibrium in a 4-point bending
test (set-up configuration is provided in drawing below), with an applied load of 1000N. The maximum stress in this set-up was less than the
yield stress for the Ti-6Al-4V…
arrow_forward
I need help with this before tomorrow’s exam if I can get all needed calculations please
arrow_forward
Please solve, engineering econ
arrow_forward
Hello tutors, help me. Just answer "Let Us Try"
arrow_forward
Help and the answers choice is
A) robin is correct
B)Pilar is correct
C)aaron is correct
D) Anthony is correct
arrow_forward
You own a wheat warehouse with a capacity of 20,000bushels. At the beginning of month 1, you have 6,000 bushels of wheat. Each month, wheat can be bought and sold at theprice per 1000 bushels given in Table 46.The sequence of events during each month is as follows:a You observe your initial stock of wheat.b You can sell any amount of wheat up to your initialstock at the current month’s selling price.c You can buy (at the current month’s buying price) asmuch wheat as you want, subject to the warehouse sizelimitation.Your goal is to formulate an LP that can be used to determine how to maximize the profit earned over the next 10months
arrow_forward
hello i hope you are fineI need your help by solving the question below. Please, please, please quickly,because I am studying now and I have exams in the coming days, so I need to do this homework in order to understand the study material and I do not have much time. I need to solve within half an hour or a little more.please please please
arrow_forward
I need problems 6 and 7 solved.
I got it solved on 2 different occasions and it is not worded correctly.
NOTE: Problem 1 is an example of how it should be answered. Below are 2 seperate links to same question asked and once again it was not answered correctly. 1. https://www.bartleby.com/questions-and-answers/it-vivch-print-reading-for-industry-228-class-date-name-review-activity-112-for-each-local-note-or-c/cadc3f7b-2c2f-4471-842b-5a84bf505857
2. https://www.bartleby.com/questions-and-answers/it-vivch-print-reading-for-industry-228-class-date-name-review-activity-112-for-each-local-note-or-c/bd5390f0-3eb6-41ff-81e2-8675809dfab1
arrow_forward
Access Pearson
Mastering Engineering
Back to my courses
Course Home
Course Home
Scores
■Review
Next >
arrow_forward
Please give a complete solution in Handwritten format.
Strictly don't use chatgpt,I need correct answer.
Engineering dynamics
arrow_forward
Please critique the attached writing assignment, discussing improtment statergies
arrow_forward
What would be the analysis of the given table or graph?
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education

Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY

Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning

Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Related Questions
- Two sport utility vehicles (SUVs) are being considered by a recent engineering graduate. Using the following data evaluate which sport utility vehicle is better. Use six attributes in your a point, overall appearance, comfort, safety, reliability, and fuel mileage. Larger scores on overall appearance, comfort, safety, reliability, and fuel mileage are preferred to smaller ones. Click the icon to view the table with data you have gathered about the SUVs. Determine attribute weights and use the nondimensional scaling technique to find the resulting set of vehicle scores. Fill in the table below. (Round to two decimal places.) More Info Attribute Price Appearance Comfort Safety Reliability Fuel mileage Relative Rank 4 253 6 1 Print Final score Alternatives SUV 1 $27,650 4 3 3 3 22 mpg SUV 1 Done Alternatives SUV 2 $21,900 3 5 4 4 18 mpg SUV 2 - Xarrow_forwardCathy Gwynn for a class project is analyzing a "Quick Shop" grocery store. The store emphasizes quick service, a limited assortment of grocery items, and higher prices. Cathy wants to see if the store hours (currently 0600 to 0100) can be changed to make the store more profitable. Time Period Daily Sales in the Time Period 0600-0700 $40 0700-0800 70 0800-0900 120 0900-1200 400 1200-1500 450 1500-1800 500 1800-2000 600 2000-2200 200 2200-2300 50 2300-2400 85 2400-0100 40 The cost ofthe groceries sold averages 65% of sales. The incremental cost to keep the store open, including the clerk's wage and other operating costs, is S23 per hour. To maximize profit, when should the store be opened, and when should it be closed?arrow_forwardThis question about Sanitary Engineering Note: please solve the question using Incremental Increase Method.arrow_forward
- Projects A and B are mutually exclusive. The minimum attractive rate of return (MARR) is 12%. Using rate of return analysis, which project should be selected? If the image fails to load here, go to https://www.dropbox.com/s/ld6wctqieu8jgwp/ROR.jpg Year 0 1 2 3 4 ROR A - $750 $200 $200 $200 $600 17.68% B - $1,150 $300 $350 $400 $700 16.44% O Project A O Project B O Both Project A and B O Select none of the project. O Insufficient information to make a decision. B-A - $400 $100 $150 $200 $100 13.69%arrow_forwardYou are a biomedical engineer working for a small orthopaedic firm that fabricates rectangular shaped fracture fixation plates from titanium alloy (model = "Ti Fix-It") materials. A recent clinical report documents some problems with the plates implanted into fractured limbs. Specifically, some plates have become permanently bent while patients are in rehab and doing partial weight bearing activities. Your boss asks you to review the technical report that was generated by the previous test engineer (whose job you now have!) and used to verify the design. The brief report states the following... "Ti Fix-It plates were manufactured from Ti-6Al-4V (grade 5) and machined into solid 150 mm long beams with a 4 mm thick and 15 mm wide cross section. Each Ti Fix-It plate was loaded in equilibrium in a 4-point bending test (set-up configuration is provided in drawing below), with an applied load of 1000N. The maximum stress in this set-up was less than the yield stress for the Ti-6Al-4V…arrow_forwardI need help with this before tomorrow’s exam if I can get all needed calculations pleasearrow_forward
- You own a wheat warehouse with a capacity of 20,000bushels. At the beginning of month 1, you have 6,000 bushels of wheat. Each month, wheat can be bought and sold at theprice per 1000 bushels given in Table 46.The sequence of events during each month is as follows:a You observe your initial stock of wheat.b You can sell any amount of wheat up to your initialstock at the current month’s selling price.c You can buy (at the current month’s buying price) asmuch wheat as you want, subject to the warehouse sizelimitation.Your goal is to formulate an LP that can be used to determine how to maximize the profit earned over the next 10monthsarrow_forwardhello i hope you are fineI need your help by solving the question below. Please, please, please quickly,because I am studying now and I have exams in the coming days, so I need to do this homework in order to understand the study material and I do not have much time. I need to solve within half an hour or a little more.please please pleasearrow_forwardI need problems 6 and 7 solved. I got it solved on 2 different occasions and it is not worded correctly. NOTE: Problem 1 is an example of how it should be answered. Below are 2 seperate links to same question asked and once again it was not answered correctly. 1. https://www.bartleby.com/questions-and-answers/it-vivch-print-reading-for-industry-228-class-date-name-review-activity-112-for-each-local-note-or-c/cadc3f7b-2c2f-4471-842b-5a84bf505857 2. https://www.bartleby.com/questions-and-answers/it-vivch-print-reading-for-industry-228-class-date-name-review-activity-112-for-each-local-note-or-c/bd5390f0-3eb6-41ff-81e2-8675809dfab1arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education

Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY

Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning

Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY