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 21cm 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.

Average Snowfall in Mount Hotham Graph showing the average precipitation (snow/rain) in Mount Hotham (2007 - 2018) Winter Summer Top Mid Bat 15 Snowfall per week (cm) Days per week May Jun Juli Aug Sep Oct Nov Apr 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 View average snowfall in Mount Hotham (graph image) Snowfall amount - Days with significant snowfall. = = Days with significant rainfall. (>5cm] (>5mm) [bar chart)