Question

In a recent year the magnitudes​ (Richter scale) of​ 10,594 earthquakes were recorded. The mean is 1.277 and the standard deviation is 0.566. Consider the magnitudes that are 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 are the magnitudes that separate the unusual magnitudes from those that are​ usual?

The lower bound earthquake magnitude is ___. ​(Type an integer or a​ decimal.)

The lower bound earthquake magnitude is ___. ​(Type an integer or a​ decimal.)

Answer 1

Sol)

Given

n = 10,594

Mean = 1.277

S.D = 0.566

Z = -2

Z = ( X - MEAN ) / SD

-2 = ( X - 1.277 ) / 0.566

-2 * 0.566 = X - 1.277

-1.132 = X - 1.277

X = 0.145

The lower bound earthquake magnitude = 0.145

Z = 2

2 = ( X - MEAN ) / SD

2 = ( X - 1.277 )/0.566

X - 1.277 = 1.132

X = 1.132 + 1.277

x = 2.409

The upper bound earthquake magnitude = 2.409

The magnitudes that seprate unusual magnitudes from usual are

0.145 < X < 2.409

X < 0.145 and X > 2.409

Magnitides between 0.145 abd 2.409 are usual remaining all magnitudes are unusual