Lab Quiz 2021_1A
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Feb 20, 2024
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MATH1021 ACCELERATED MATHEMATICS FOR ENGINEERS
Lab Test (a)
Semester 1, 2021
Marks: /20
Declaration
: I hereby undertake not to discuss or divulge the content or format of the test paper with any other person until all tests have been written, and declare that I have no prior
knowledge of the contents of the test paper.
I unconditionally accept any action that may be taken should Curtin University consider that an infringement of the statute No. 10 of the Student Disciplinary Statute has occurred.
Name
: ID
.
Signature
: Date
: / / 2021
Instructions: Download the “Lab template (word file to copy-paste answers into).docx” Word
document from Assessment tab-> Lab assessment on Blackboard and save it in your StudentID
-drive
directory (the directory with your student ID) as Your Name Your ID
, for example: Joe Smith
2456892.docx
. Write your test solutions in this Word document, and save the file regularly. All
questions require you to copy the commands/output from R/RStudio and paste it into this
document. Copying and pasting only the solution is not sufficient, all R commands used in making
your calculations must be included in your document to obtain full marks. Once you have completed
the test, you must submit two documents:
Your final Word document with solutions should be submitted through Turnitin on
Blackboard
. The link for assessment submission can be found under Assessment tab-> Lab
assessment-> Lab assessment submission. The Submission Title should be in the form of
Tutor Day Time
(so for example, Heather Wednesday 10am). After submitting the file to
Turnitin you should receive a receipt to say it has been submitted correctly. To double-check
this step has been completed, go back into the link at Lab assessment submission and check
that your submission is there and that you have submitted the correct file.
The physical test paper, to be completed with your name, student ID, signature, and date,
must be submitted in person
to your tutor before you leave the room. Question 1 [12 Marks]
Using the following R commands, generate a sample data set of size 30 that simulates the weights of
10 year old boys in kilograms. set.seed(1000)
weight
<-
rnorm(30, 24, 1.2)
This saves the data as a variable called weight
. (The set.seed command is to make sure that the data
set you generated will match the data set used in the solution.) Do all of the following questions using
R.
a)
Draw a histogram for the weight data.
.
[2 marks]
b)
Obtain the five number summary. Identify clearly the five numbers as min, max, etc. [2 marks]
c)
What is the inter-quartile range?
[1 mark]
d)
Obtain a box plot for the variable with appropriate labels. Are there any outliers?
[2 marks]
e)
Find the sample mean x
and sample variance s
2
of the weights.
[2 marks]
f)
It is known that the sample mean x
satisfies a normal distribution. If it is assumed that the population standard deviation is 1.2, find the 93% confidence interval for the population mean µ.
[3 marks]
Question 2 [8 Marks]
A fair die is rolled 50 times. Let X denote the number of times ‘1’ appeared on top.
a)
Find the probability P
(
5
≤ X ≤
10
)
.
[2 marks]
b)
Find the smallest positive integer k
such that P
(
X ≤k
)
≥
0.5
.
[2 marks]
c)
What are the mean and standard deviation of X?
[2 marks]
d)
Simulate this experiment by randomly generating the corresponding data a 1000 times. Compute the mean and standard deviation of the generated data and compare with your answers to (c).
[2 marks]
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