## 6.5 **Optional**: Working with normal distributions

*(Answers are available in Sect. A.6)*

The Southern Oscillation Index (SOI) is a
unitless^{5}
climatological measure that is easily computed,
and has been shown to be related to the weather conditions in eastern Australia (Stone and Auliciems 1992).

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

Stone, Roger C., and A. Auliciems. 1992. “soi Phase Relationships with Rainfall in Eastern Australia.” *International Journal of Climatology* 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.↩︎