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.↩︎