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.