5.6 Optional: Working with normal distributions
This question is optional; for example, if you need more practice, or you are studying for the exam.
(Answers are available in Sect. A.6)
This question has a video solution in the online book, so you can hear and see the solution.
The Southern Oscillation Index (SOI) is a unitless2 climatological measure that is easily computed, and has been shown to be related to the weather conditions in eastern Australia (Stone and Auliciems 1992; Dunn 2001).
The daily SOI has an approximate normal distribution, and is designed to have a mean of 0 and a standard deviation of 10.
- Draw a rough, labelled sketch of the theoretical distribution of the SOI values.
- What is the probability that the daily SOI exceeds \(20\)?
- What are the odds that the daily SOI exceeds 20?
- What is the probability that the daily SOI is less than \(-25\)?
- What is the probability that the daily SOI is greater than \(-12\)?
- What is the probability that the daily SOI is between \(-10\) and \(20\)?
- The SOI is less than what value about 80% of the time?
- The SOI is greater than what value about 35% of the time?