This assignment is based on the second half of the Intro to Statistics & Probabi


This assignment is based on the second half of the Intro to Statistics & Probability section
of the course.
Please include your R code and outputs for each of the below questions wherever
needed.
Some ideas for how you can most easily do this:
• If working in Jupyter: Make a Jupyter notebook document for each separate question
below, and intersperse the text with code as needed.
• If working in R/RStudio: Copy-paste your code/outputs into a Word document along
with your responses to the questions, and save it as a PDF.
• Alternatively, if you know how to work with RMarkdown: Save your code and responses
together in an RMarkdown document and save them as a PDF.
Other important policies on assignment submissions:
• Please write each question on a separate page!
• PLEASE SHOW ALL YOUR WORK TO GET FULL MARKS!
(4 marks) Consider the following (fictional) probability model, for the number of cars
in Canadian households:
Number of cars: 0 1 2 3 4 5 6
Probability: 0.02 0.33 0.39 0.15 0.08 0.02 0.01
We suppose, for the sake of this question, that there are no households in Canada with
more than 6 cars.
(a) Is this a valid probability model? Check that the values in the table satisfy the
two Probability Rules.
(b) What proportion of Canadian households don’t have zero cars (i.e., they have at
least one car)? Show your work.
(c) A developer builds townhouses with two-car garages. What proportion of Canadian households have more cars than this garage can hold?
(d) You pick a Canadian household at random. What is the probability that this
household has an odd number of cars?
(6 marks) A 1987 study found that the distribution of weights for the population of
males in the United States was
approximately normally distributed with mean µ =
172.2 pounds and standard deviation σ = 29.8 pounds.
(a) Create a rough sketch of this Normal distribution, by hand. It doesn’t have to
look perfect! However, make sure that the general shape is correct, and that you
have labelled the mean and the standard deviation somewhere in your figure.
(b) By calculator, approximate the probability that a randomly selected man (in 1987)
weighs more than 202.0 pounds.
(c) By calculator, approximately how much would a man have to weigh (in 1987) in order
to be in the 2.5th percentile of male weights? (Note: An individual is said to be
“in the 2.5th percentile” if 2.5% of individuals weigh less than him.)
(d) The same study found that the average weight of women in the sample was 144.2
pounds. Use R to find the
the probability that a randomly chosen man (in 1987)
weighs more than this amount.
(2 marks) Suppose a different study, taken in a different country, found that weights in
that country were not normally distributed! In this second study, the weights of men
had a mean of 182.1 pounds and a median of 173.1 pounds. The first and third quartiles
were 152.0 pounds and 204.5 pounds, respectively.
(a) What can you say about the shape of this distribution, based on these numbers
alone?
(b) By hand, find the probability that a randomly selected man from this country
weighs between 173.1 pounds and 204.5 pounds.


Leave a Reply