ECON 327 Programming Questions

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ECON 327 Assignment 3
Winter Term 1, 2022-2023
Instructions
This assignment contains 4 questions and must be completed with R. Write down
your answers and codes in a R Markdown file (.rmd) using the RStudio, then
generate a PDF file. Upload the R Markdown file and the PDF file to Canvas.
Please upload all files to Canvas by Sunday, November 27th (11:59 pm Vancouver
Time).
Late submissions, for any reason, will not be accepted. If you are unable to complete
this assignment for health reasons, you must provide a valid doctorànote to shift its
weight to your ?nal exam.
Question 1 [8 points]
Generate 10 random numbers from a uniform distribution on [0,10]. Also, find the maximum and
minimum values.
(a) For normal (0,1), find a number ?? ? solving P (Z ? ?? ? ) = .05.
(b) For normal (0,1), find a number ?? ? solving P (??? ? ? Z ? ?? ? ) = .05
Question 2 [8 points]
The distribution of a professoràexam scores is normally distributed with a mean of 60 points and
a standard deviation of 15 points. The professor promises his students that the top 20% of the
scores will receive a grade of A in his class.
(a) What is the minimum score you must achieve to receive an A in the class?
(b) Sketch the graph and shade the concerned region.
Question 3 [9 points]
Let ??? be the mean of a random sample of size 50 drawn from a population with mean 112 and
standard deviation 40.
(a) Find the mean and standard deviation of ???.
(b) Find the probability that ??? assumes a value between 110 and 114.
(c) Find the probability that ??? assumes a value greater than 113.
Question 4 [15 points]
A random sample of size 30 is obtained from a normally distributed population with population
mean 500 and a standard deviation of 100
(a) Construct a sampling distribution of the mean that has 1000 samples
(b) Calculate its Mean, Variance and Standard Error.
(c) Make a plot that shows the histograms for each of your 1000 samples
(d) using 3 different sample sizes (10, 100, 500), make three different histograms with normal
curve. what happens to the shape of the histogram with increasing sample size?
(e) Describe the shape of this sampling distribution and compare the sampling distribution for
all the sample sizes.
(f) What is the probability of getting a mean of 460?

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