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In: Statistics and Probability

Suppose the average yearly rainfall in Sydney Australia, is about 137mm and the standard deviation is...

Suppose the average yearly rainfall in Sydney Australia, is about 137mm and the standard deviation is about 10mm. Use normal approximation to find the probability that the yearly rainfall is less than 110mm.

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Expert Solution

Let X : The yearly rainfall in Sydney Australia

Given, X follows Normal( = 137, =10)

To find the probability that the yearly rainfall is less than 110mm, i.e., P(X<110)

Using normal appproximation, i.e., Central Limit Theorem, which states that,

Thus,

(from Z-table)

Therefore, the probability that the yearly rainfall in Sydney Australia is less than 110mm is 0.0035

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z-table for reference:

orchestra answered 2 years ago
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