(2)

Step 1:

(a)

Let the magnitude of earthquake is $\"\"$ .

The mean of earthquake is 1.184.

The standard deviation of earthquake is 0.587.

Find the percentage of earthquake with magnitudes less than 2.000.

$\"\"$ .

Now calculate the Z-score for the given probability.

$\"\"$ ,

Where $\"\"$ is the magnitude of eartqua

$\"\"$ is the mean and $\"\"$ is the standard deviation.

$\"\"$

From z - score table the percentage is $\"\"$

(b)

(2)

Step 1:

(a)

Let the magnitude of earthquake is $\"\"$ .

The mean of earthquake is 1.184.

The standard deviation of earthquake is 0.587.

Find the percentage of earthquake with magnitudes above 4.

$\"\"$ .

Now calculate the Z-score for the given probability.

$\"\"$ ,

Where $\"\"$ is the magnitude of eartqua

$\"\"$ is the mean and $\"\"$ is the standard deviation.

Percentage of earthquake with magnitudes above 4 is $\"\"$ .

$\"\"$

From z - score table the percentage is $\"\"$

$\"\"$

Percentage of earthquake with magnitudes above 4 is 0.00001%. \ \

(2)

Step 1:

(c)

Let the magnitude of earthquake is $\"\"$ .

The mean of earthquake is 1.184.

The standard deviation of earthquake is 0.587.

Find the 95th percentile of earthquake magnitudes.

From the z - score table :

z - score value corresponds to 95th percentile is 1.644. \ \

Now calculate the earthquake magnitudes for the given percentile.

$\"\"$ ,

Where $\"\"$ is the magnitude of earthquake.

$\"\"$ is the mean and $\"\"$ is the standard deviation.

$\"\"$

Percentage of earthquake with magnitudes above 4 is $\"\"$ .

$\"\"$

From z - score table the percentage is $\"\"$

$\"\"$

Percentage of earthquake with magnitudes above 4 is 0.00001%.