MTH 116 Assignment 1 (Group Work) W24
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Centennial College *
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Mathematics
Date
Feb 20, 2024
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MTH 116 Group Work (Assignment 1) Test 1 Formulae Sheet and z-table (normal distribution table) are enclosed in this file. This group work is to be used for both group work and revision towards your Test 1. FOR GROUP WORK:
Submit your solution for Questions 1, 2b, 3a to 3d, 4 (all the questions), 5(a, b, c, e, and g) and 6A to your group leaders for coordination. FOR PREPARATION FOR TEST
: The other questions can be discussed in your groups in preparation for the Test. GROUP WORK INSTRUCTIONS Due date for group members to submit their contribution (their own answers for group work questions) to
their group leaders is Friday January 26, 2024.
Please look for your name on the list below and you will see the name and email of your group leaders. Send your email address to your group leaders to connect with the group. There are two groups in all. Everyone in this course can access the group work on ecentennial by clicking on the CONTENT tab on your MTH 116 home page, then click on GROUP LIST/GROUP WORK folder, you will see the group work and the group list. Please write your answers down and send your solutions to your group leader if you will not be present during the group discussion to demonstrate your participation in the group activity. Failure to do this will result in you being awarded a zero grade for this group work. The Group Leaders will coordinate the discussion within the group and once you all agree on what the solution for each question should be, the group leaders will scan and upload the agreed solution to the GROUP WORK folder on ecentennial by clicking on ASSESSMENTS tab, then ASSIGNMENTS folder and finally the Group Work 1 folder (ONLY GROUP LEADERS WILL BE ABLE TO SUBMIT INTO THIS FOLDER). The grade given to the work submitted by the group leaders will be given to ONLY those that participated in the group work. Non-participants will be
graded zero. Group Leaders are to forward the names of those that participated with the submission. Please do not send me individual solutions because it is called group work. I will only grade the agreed solution by participants of the group activity as uploaded by the group leader. The deadline for the group leader to upload the agreed solution is Monday January 29, 2024.
1) The following table summarizes 348 films from 2010 that have been classified into a genre and have a MPAA rating. G PG PG-13 R Total Action/Adventure 3 18
18 14
53 Comedy 2 18 29 41
90
Documentary 4 8 8
9 29 Drama 0 16 36 65 117
Musical 0 2
2
0 4 Suspense/Thriller/Horror 0 1 13 41 55
Total 9
63 106
170 348 Source: www.the-numbers.com/ a)
Complete the table by writing the missing marginal and joint distributions (5 marks) b)
What percentage of these films were rated R? (1 mark) c)
What percentage of these films were rated PG-13? (1 mark) d)
What percentage of R- rated films were Drama? (1 mark) e)
What percentage of Drama were rated R? (1 mark) f)
What percentage of Action/Adventure were either rated PG or R? (1 mark) g)
What percentage of PG-13 rated films were either Comedy or Drama? (1 mark) h)
What percentage of these films were Drama and rated R? (1 mark) i)
What percentage of these films were rated PG-13 and R? (1 mark) j)
What percentage of these films were Comedy and Musical? (1 mark)
2) Tables, frequency and relative frequency distribution exercises
Some drivers were asked what type of driver’s license they have. They replied as follows: G1, G, M1, G1, G, A, G2, G, B, A, G1, M1, G2, A, G, G2, G, M1, A, G, G1, M1, G, G, B a) Construct a frequency table for the data above (2 marks) b) Determine the relative frequency distribution for the classes of driver’s license.(10 marks) c) Which is the modal license class? (1 mark) d) What type of graph will be most appropriate for this distribution and why? (2 marks) e) Name the type of graph that will not be appropriate for this distribution and state your reason in one sentence. (2 marks) 3) Stem-and-leaf plot and Boxplot exercises
Consider the following set of data and answer the questions that follows: 18 28 28 28 37 31 24 29 8 27 24 12 21 32 27 24 23 33 31 29 36 a)
Construct a stem-and-leaf plot without splitting the stems (2 marks) b)
Is the distribution uni-modal or bimodal? (1 mark) c)
Construct a stem-and-leaf plot by splitting the stems and put the leaves 0-4 on one line and 5-9 on another line. (2 marks) d)
Find the 5-Number Summary {min, 𝑄
1 (𝑃
25
)
, 𝑄
2 (𝑃
50
)
, 𝑄
3 (𝑃
75
)
, max}, IQR, lower boundary and upper boundary of the data set above. (8 marks) e)
Use the information you got from question 3d to construct a boxplot in the graph provided below. (2 marks)
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4) Measures of central tendencies and variation exercises
Consider the following set of data and answer the questions that follows: 10, 11, 14, 12, 14, 12, 11, 12, 13, 12, 16, 13. a) What is the mean? (2 marks) b) What is the mode based on what you think the histogram looks like? (1 mark) c) What is median? (1 mark) d) Find Q1, Q2, Q3, and IQR (4 marks) e) Find the Range (1 mark) f)
With the aid of the table below or any other preferred approach, calculate the standard deviation (Round to one more decimal than the mean) (6 marks) Data or (
𝑥)
(𝐷𝑎𝑡𝑎 − 𝑀𝑒𝑎𝑛)
or (
𝑥 − 𝑥̅)
(𝐷𝑎𝑡𝑎 − 𝑀𝑒𝑎𝑛)
2
or (𝑥 − 𝑥̅)
2
Total g) If I subtract 4 from each of the data in the data set provided, what would be the value of the new (You must state the values for each) (8 marks)
(i) mean (ii) median (iii) Q1 (iv) Q2 (v) Q3 (vi) range (vii) Standard deviation (viii) IQR h) If I multiply each of the data in the data set provided by 1.5, what would be the value of the new (You must state the values for each) (8 marks) (i) mean (ii) median (iii) Q1 (iv) Q2 (v) Q3 (vi) range (vii) Standard deviation (viii) IQR 5) Z-Scores, 68-95-99.7 Rule, Normal Distribution Table (z-Table), Normal percentiles
Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested sometime ago predicted a mean of 23.6 mpg and a standard deviation of 5.6 mpg for highway driving. Assume that a Normal model can be applied a) In what interval would you expect the central 68% of autos to be found using what the 68-95-99.7 Rule predicts. (Show this area on the normal distribution below
) b) About what percent of autos should get between
11 mpg and 32 mpg? (Make a sketch of the area
concerned on the normal distribution) (Use z-
Table) 2 2
c) About what percent of autos should get between
26 mpg and 38 mpg? (Make a sketch of the area
concerned on the normal distribution) (Use z-
Table) d) About what percent of autos should get between
8 mpg and 19.6 mpg? (Make a sketch of the area
concerned on the normal distribution) (Use z-
Table) e) About what percent of autos should get less than 11 mpg? (Make a sketch of the area concerned on the normal distribution) (Use z-Table)
2 2 2
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f)
About what percent of autos should get more than 39 mpg? (Make a sketch of the area concerned on the normal distribution) (Use z-Table)
g) What is the value in mpg of the data that will have a z - score of 1.95? (Round your answer to one decimal if necessary) h) What is the value in mpg of the data that will have a z - score of -2.40? (Round your answer to one decimal if necessary) 6) Scatterplot, correlation coefficient (r), Regression equation and R-squared (R
2
) value
A)
Given the following information: 𝑥̅ = 2 𝑠
𝑥 = 0.06, 𝑦̅ = 7.2, 𝑠
𝑦 = 1.2, 𝑟 = −0.4 i)
Find the values of 𝑏
0
and 𝑏
1
(Rounded to three decimals). Write the equation of the
Least Squares line 𝑦̂ = 𝑏
0 + 𝑏
1
𝑥
2 2 2 3
ii)
Find the 𝑅
2
value
1 iii)
What percent of variation in the data can be explained (or accounted for) by the regression line? iv)
Assuming 𝑅
2 = 70.2%
what would be the value of the correlation coefficient (r)
1 B)
Given the following information: 𝑥̅ = 12 𝑠
𝑥 = 6, 𝑟 = −0.8 and 𝑦̂ = 200 − 4𝑥
i)
Find the values of 𝑦̅
and 𝑠
𝑦
(Rounded to three decimals).
ii)
Find the 𝑅
2
value
1 1
4
iii)
What percent of variation in the data can be explained (or accounted for) by the regression line? C)
The owner of a Bookstore wants to study the relationship between the number of sales people working in the bookstore and sales. Using the randomly selected data in the table below, answer the questions that follow. Number of Sales
People Working Sales (in
thousands) 𝒚̂ = 𝟖. 𝟖𝟒 + 𝟎. 𝟕𝟒𝟓 𝒙, 𝑹
𝟐 = 𝟎. 𝟕𝟑𝟗
2 8 3 9 6 14 10 19 11 21 14 20 20 20 a)
If we want to estimate sales based on the number of sales people working, which
variable is the independent variable and which is the dependent variable? b)
What is the value of the correlation coefficient (r)? Comment on the strength and direction of the correlation. 2 c)
What percent of the variation in Sales can be explained by the regression line? 1 1
1
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d)
Estimate the sales if 13 sales people were working 1 e)
If the observed sales for 13 people were $19000, what is the residual? 1
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