6.8 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.↩︎