Statistics 101-The Australian Bureau of Meteorology uses the monthly

Statistics  101-The Australian Bureau of Meteorology uses the monthly

Subject: Mathematics    / Statistics
Question

4.38 The Australian Bureau of Meteorology uses the monthly air-pressure difference between Tahiti and Darwin, Australia, to calculate the Southern Oscillation Index:

SOI ¼ 10(X m)/s, where X is the air-pressure difference in the current month, m is the average value of X for this month, and s is the standard deviation of X for this month. Negative values of the SOI indicate an El Nin˜o episode, which is usually accompanied by less than usual rainfall over eastern and northern Australia; positive values of the SOI indicate a La Nin˜a episode, which is usually accompanied by more than usual rainfall over eastern and northern Australia.

Suppose that X is normally distributed with a mean of m and a standard deviation of s. Explain why you believe that the probability of an SOI reading as low as 22.8, which occurred in 1994, is closer to 1.1 10 15, 0.011, or 0.110.