In a recent year the magnitudes (Richter scale) of 10.594 earthquakes were recor

Question

In a recent year the magnitudes (Richter scale) of 10.594 earthquakes were recorded. The mean is 1.296 and the standard deviation is 0.573. Consider the magnitudes that arc unusual. What are the magnitudes that separate the unusual magnitudes from those that are usual? (Consider a value to be unusual if its z score is less than -2 or greater than 2.) What arc the magnitudes that separate the unusual magnitudes from those that are usual? The lower bound earthquake magnitude is squarebox. (type an integer or a decimal).

Explanation / Answer

Here N = 10594, Mean = 1.296 and St. Dev = 0.573. It is defined that it the Z-score is beyond the limit of -2 and +2 i.e. beyond the 95% limit, the earthquake is unusual. Now Z is defined as

Z = (x - µ) /

P( -2<Z<2) = 0.9544

P(0<Z<2) = 0.4772

Here µ = 1.296, = 0.573

(x - 1.296) / o.573 = 2

Implies x = 1.296 + 2 * 0.573

= 2.442

So, the earthquake of magitude 2.442 and above will be treated as unusual.

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