6.6 Optional questions
These questions are optional; e.g., if you need more practice, or you are studying for the exam. (Answers appear in Sect. A.6.)
6.6.1 (Optional) Working with normal distributions
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?
References
Dunn PK. Bootstrap confidence intervals for predicted rainfall quantiles. International Journal of Climatology. 2001;21(1):89–94.
Stone RC, Auliciems A. soi phase relationships with rainfall in eastern Australia. International Journal of Climatology. 1992;12:625–36.
That is, it is not measured in kilograms or seconds etc. It is just a number; in fact, it is a bit like a z-score.↩︎