Question 3 – Normal probability models [Total: 9 marks] You want to go to the snow in August, but
this is dependent on whether you can get
accommodation at short notice! Before
you plan your trip you want to know the
odds of having fresh powder snow on
your arrival. After some research, you
decide to go to Mount Hotham, since
https://www. snowforecast. com/resorts/MountHotham/history touts that: “The snowiest
week in Mount Hotham is week 1 of
August. There are typically 4.1 snowy
days during this week with 21 cm of
snowfall” (see figure below from that
website). That all sounds great!
The number of ‘predominant snowfall’ days (defined when snowfall is ≥ 5 cm) in the 31 days of August
varies according to a roughly Normal distribution with a mean of 15 days of snowfall across that
particular month and standard deviation of 5 days.

I. If you were to choose a year at random, what is the probability that the year you choose has
greater than 15 days of predominant snowfall in August?
[3 marks]
II. What is the proportion of years where August’s monthly snowfall falls between 10 and 15 days?
[3marks]
III. Considering the 20% snowiest Augusts, up to what number of days of predominant snow (≥ 5
cm) would these snowiest August receive?
[3 marks]
*Accompany each of the answers above with a shaded in density curve to demonstrate your understanding of
the question. You can draw, copy and paste these images OR use software.
Marking Criteria for Question 3:
You may use any of the tools that you have been shown to determine the necessary probabilities. For
full marks, you need to demonstrate understanding of the probability conceptsinvolved in each part of
this question, so provide a density curve, workings (the calculation of relevant z-scores and probabilities)
as well as a very brief relevant written statement interpreting the answer to the question (so place the
numerical answer into a correct full statement showing you understand what it means).
No marks awarded for the correct answer without working out or explain how the answer was
determined.