The Australian Bureau of Meteorology uses the monthly air-pressure difference be

Question

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.

Explanation / Answer

we are given that the soi formula is

10* (x-mu)/sd

so which is 10 times of normal z score fomula ,

so if we calculate '

-22.8 = 10* (x-mu)/sd

(x-mu)/sd = -2.28 and then check for this value in the z table we get

P ( Z<2.28 )=1P ( Z<2.28 )=10.9887=0.0113

hence woiuld belive it be clsoe to 0.011

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