Week 1 Homework
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School
Georgia Institute Of Technology *
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Course
6242
Subject
Statistics
Date
Feb 20, 2024
Type
docx
Pages
11
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Week 1 Homework
Due
Jan 19 at 8:59pm
Points
12
Questions
12
Available
Jan 12 at 5am - Jan 22 at 8:59pm
Time Limit
None
Instructions
Please answer all the questions below.
This quiz was locked Jan 22 at 8:59pm.
Attempt History
Attempt
Time
Score
LATEST
Attempt 1
50 minutes
12 out of 12
Score for this quiz:
12
out of 12
Submitted Jan 12 at 8:51pm
This attempt took 50 minutes.
Question 1
1
/ 1
pts
(Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having
height
ℎ
0 = 1000 feet. You're a strong bloke, so the initial downward velocity
is �0 = -100 feet/sec (slightly under 70 miles/hr). Further, in this neck of the
woods, it turns out there is no friction in the atmosphere - amazing! Now you
remember from your Baby Physics class that the height after time � is
ℎ
(�)=
ℎ
0+�0�−16�2
When does the rock hit the ground?
a. -11.625 sec
b. 2 sec
Correct!
c. 5.375 sec
Set
0=
ℎ
(�)=1000−100�−16�2,
and solve for t. Quadratics are easy:
�=−�±�2−4��2�=100±1002+4(16)(1000)2(−16)=−100±272.032=5.375,
which we take as the answer since the negative answer doesn't make practical sense.
d. 11.625 sec
e. 10 sec
Set
0=
ℎ
(�)=1000−100�−16�2,
and solve for t. Quadratics are easy:
�=−�±�2−4��2�=100±1002+4(16)
(1000)2(−16)=−100±272.032=5.375,
which we take as the answer since the negative answer doesn't make practical sense.
Question 2
1
/ 1
pts
(Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between customer arrivals are independent, identically distributed Exp(λ = 2/hr) random variables; and the service times are i.i.d. Exp(µ = 3/hr). Unfortunately, if a potential arriving customer sees that the server is occupied, he gets mad and leaves the system. Thus, the system can have either 0 or 1 customer in it at any time. This is what’s known as an M/M/1/1 queue. If �(�) denotes the probability that a customer is being served at time t, trust me that it can be shown that
�(�)=��+�+[�(0)−��+�]�−(�+�)�.
If the system is empty at time 0, i.e., �(0)=0, what is the probability that there will be no people in the system at time 1 hr?
a. 1
b. 2/3
c. 0.397
Correct!
d. 0.603
At time �=1, we have
1−�(�)=1−��+�−[�(0)−��+�]�−(�+�)�=��+�−[�(0)−��+�]�−
(�+�)�=32+3−[0−25]�−(5)(1)=0.603
At time �=1, we have
1−�(�)=1−��+�−[�(0)−��+�]�−(�+�)�=��+�−
[�(0)−��+�]�−(�+�)�=32+3−[0−25]�−(5)(1)=0.603
Question 3
1
/ 1
pts
(Lesson 1.4: History.) Harry Markowitz (one of the big wheels in simulation language development) won his Nobel Prize for portfolio theory in 1990, though the work that earned him the award was conducted much earlier in the 1950s. Who won the 1990 Prize with him? You are allowed to look this one up.
Correct!
a. Merton Miller and William Sharpe
for accomplishments in related (but slightly different) subject areas.
b. Henry Kissinger
c. Albert Einstein
d. Subrahmanyan Chandrasekhar
for accomplishments in related (but slightly different) subject areas.
Question 4
1
/ 1
pts
(Lesson 1.5: Applications.) Which of the following situations might be good candidates to use simulation? (There may be more than one correct answer.)
a. We put $5000 into a savings account paying 2% continuously compounded interest per year, and we are interested in determining the account's value in 5 years.
Correct!
b. We are interested in investing one half of our portfolio in fixed-interest U.S. bonds and the remaining half in a stock market equity index. We have some information concerning the distribution of stock market returns, but we
do not really know what will happen in the market with certainty.
Correct!
c. We have a new strategy for baseball batting orders, and we would like to know if this strategy beats other commonly used batting orders (e.g., a fast guy bats first, a big, strong guy bats fourth, etc.). We have information on the performance of the various team members, but there’s a lot of randomness in baseball.
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Related Questions
(C) Use the adjusted seasonal indexes given in part (a) to adjust the forecasts developed in part (b) to account for the effect of season. (Round your answers to one decimal place.)
forecast for quarter 1: 15.7
forecast for quarter 2: 26.7
forecast for quarter 3: 47.6
forecast for quarter 4: 15.3
The answers for this questions came back as wrong. I am unsure how else I would solve it.
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Your Mark:
OUT OF
2
Instruction: There are two parts (a to b) to this question. Answer all of them. Fill in your answer in the coloured box below.
Question 1
The administrator of the undergraduate program of a University is interested in determining the post-program employment of the grads. The survey asked a series of questions including the following: 1) What is your post-program employment position? 2) What is your post-program employment location (country)? 3) What is your post-program employment position base salary in dollars (rounded to the nearest thousands)? 4) How many months after graduation did you find the job? A random sample of 50 graduates' responses are collected.
a. Identify how many cases are collected.
b. Identify whether the responses…
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chapter 5
10. A buyer plans to purchase 250 towels for the store's harvest sale and to retail each towel for $7.50. He has placed an order for 128 towels that cost $3.25 each. What is the most he can pay for each of the remaining towels if he wishes to average a 42% markup?
Present your answer with a dollar-sign, comma separator, and rounded to the penny (i.e. $1,250.88).
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Only parts d and e will be solved.
A social media publicist working for a popular video game developer company wants to study the social media content viewing habits of Youtube platform users. A random sample of 40 users is selected, and each user is instructed to keep a detailed record of all content viewing in a particular month. The results are as follows:• Viewing time per month: ? = 15.3 hours, S = 3.8 hours.• 27 users watch the content published on evening on at least three nights in a month.a. Construct a 90% confidence interval estimate for the mean amount of content watched per month on Youtube.b. Construct a 90% confidence interval estimate for the population proportion who watch the evening content on at least three nights per month.Suppose that the social media publicist wants to take another survey in a different platform. Answer these questions:c. What sample size is required to be 90% confident of estimating the population mean viewing time to within ± 2 hours assuming…
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Question 3
Fiona and Franny were comparing balances and interest rates on their respective car loans. At the end of last month Fiona still owed $12,300 and is paying 3.6% interest and Franny still owed $9,500 and is paying 4.66% interest. Fiona said she was going to have a larger interest charge than Franny this month, and Franny said she was going to have a larger interest charge this than Fiona. Which one is correct?
Group of answer choices
Fiona is correct since her interest charge this month is $36.89 and Fiona's is $36.90
Fiona is correct since her interest charge this month is $36.90 and Franny's is $36.89
Franny is correct since her interest charge this month is $36.89 and Fiona's is $36.90
Franny is correct since her interest charge this month is $36.90 and Fiona's is $36.89
Neither are correct since both will have the same interest charge this month.
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Question No. 3:
The average time that Italy commute to work is 23.15 minutes (Best 4 Tourist Places, June 15, 2020). The average commute times in minutes for 18 cities are given in Table 3.1.
Table 3.1
City
Time (minutes)
Rome
24.9
Milan
26.8
Naples
26.2
Turin
28.1
Palermo
31.7
Genoa
25.8
Bologna
23.3
Florence
32.1
Bari
28.5
Catania
24.4
Verona
29.3
Venice
24.8
Messina
38.1
Padua
28.3
Trieste
28.4
Taranto
24.6
Prato
20.1
Modena
23.4
a) What is the mean commute time for these 18 cities?
b) What is the median commute time for these 18 cities?
c) What is the mode for these 18 cities?
d) What is the variance and standard deviation of commute times for these 18 cities?
e) Find the z – score value of commute time for…
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Question No. 3:
The average time that Italy commute to work is 23.15 minutes (Best 4 Tourist Places, June 15, 2020). The average commute times in minutes for 18 cities are given in Table 3.1.
Table 3.1
City
Time (minutes)
Rome
24.9
Milan
26.8
Naples
26.2
Turin
28.1
Palermo
31.7
Genoa
25.8
Bologna
23.3
Florence
32.1
Bari
28.5
Catania
24.4
Verona
29.3
Venice
24.8
Messina
38.1
Padua
28.3
Trieste
28.4
Taranto
24.6
Prato
20.1
Modena
23.4
a) What is the variance and standard deviation of commute times for these 18 cities?
b) Find the z – score value of commute time for these 18 cities.
c) Find 28th and 77th Percentile of commute times for these 18 cities.
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Question 2
The past records of a supermarket show that its customers spend an average of $65 per visit at this store. Recently the management of the store initiated a promotional campaign according to which each customer receives points based on the total money spent at the store, and these points can be used to buy products at the store. The management expects that as a result of this campaign, the customers should be encouraged to spend more money at the store. To check whether this is true, the manager of the store took a sample of 12 customers who visited the store. The following data give the money (in dollars) spent by these customers at this supermarket during their visits. 88 69 141 28 106 45 32 51 78 54 110 83 Assume that the money spent by all customers at this supermarket has a normal distribution. Using the 5% significance level, can you conclude that the mean amount of money spend by all customers at this supermarket after the campaign was started is more than $65?
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An elementary education researcher was interested in seeing how the color used to make corrections on students’ papers affected their self-esteem. He assembled first graders and asked them to take a third-grade math test. He told the first graders that the test would be very difficult for them and they might not get very many answers right, but he needed their help. After the students were each called into a room to take the test alone, he pretended to grade it. Everyone had 25% of their answers marked wrong. For half the kids, these answers were marked with red ink and for the other half, the “incorrect” answers were marked with pencil. Each child then took a self-esteem inventory on which higher scores indicate more self-esteem. The 17 red ink kids had a mean of 23.00 (s = 5.00); the 10 pencil kids had a mean score of 29.00 (s = 5.00). Using s2pooled =25.0, sM1−M2 =1.99, and alpha of .05 and a two tailed test, determine if there is a difference in self-esteem.
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answer the following quaries
4. A survey was conducted to 100 students to determine how much time they spend for studying before taking a major examination. The observations are between 90 and 270 minutes. How many classes will you recommend? What is the class interval?
5. A sari-sari storeowner monitors his daily sales for a period of 30 days. The following are his daily sales:
560 960 260 900 700 1020
370 940 340 400 795 240
200 390 100 500 890 900
250 450 1010 650 800 450
250 450 890 695 749 360
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I need help in task 3 , i provided the previous tasks if needed
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- Only parts d and e will be solved. A social media publicist working for a popular video game developer company wants to study the social media content viewing habits of Youtube platform users. A random sample of 40 users is selected, and each user is instructed to keep a detailed record of all content viewing in a particular month. The results are as follows:• Viewing time per month: ? = 15.3 hours, S = 3.8 hours.• 27 users watch the content published on evening on at least three nights in a month.a. Construct a 90% confidence interval estimate for the mean amount of content watched per month on Youtube.b. Construct a 90% confidence interval estimate for the population proportion who watch the evening content on at least three nights per month.Suppose that the social media publicist wants to take another survey in a different platform. Answer these questions:c. What sample size is required to be 90% confident of estimating the population mean viewing time to within ± 2 hours assuming…arrow_forwardQuestion 3 Fiona and Franny were comparing balances and interest rates on their respective car loans. At the end of last month Fiona still owed $12,300 and is paying 3.6% interest and Franny still owed $9,500 and is paying 4.66% interest. Fiona said she was going to have a larger interest charge than Franny this month, and Franny said she was going to have a larger interest charge this than Fiona. Which one is correct? Group of answer choices Fiona is correct since her interest charge this month is $36.89 and Fiona's is $36.90 Fiona is correct since her interest charge this month is $36.90 and Franny's is $36.89 Franny is correct since her interest charge this month is $36.89 and Fiona's is $36.90 Franny is correct since her interest charge this month is $36.90 and Fiona's is $36.89 Neither are correct since both will have the same interest charge this month.arrow_forwardQuestion No. 3: The average time that Italy commute to work is 23.15 minutes (Best 4 Tourist Places, June 15, 2020). The average commute times in minutes for 18 cities are given in Table 3.1. Table 3.1 City Time (minutes) Rome 24.9 Milan 26.8 Naples 26.2 Turin 28.1 Palermo 31.7 Genoa 25.8 Bologna 23.3 Florence 32.1 Bari 28.5 Catania 24.4 Verona 29.3 Venice 24.8 Messina 38.1 Padua 28.3 Trieste 28.4 Taranto 24.6 Prato 20.1 Modena 23.4 a) What is the mean commute time for these 18 cities? b) What is the median commute time for these 18 cities? c) What is the mode for these 18 cities? d) What is the variance and standard deviation of commute times for these 18 cities? e) Find the z – score value of commute time for…arrow_forward
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