The Richter scale magnitude of earthquakes are normally dist

The Richter scale magnitude of earthquakes are normally distributed with a mean of 1.184 and a standard deviation of 0.587.

Earthquakes below 2.000 are considered microearthquakes and are not felt. What proportion are microearthquakes?  

What proportion are above 3.000 on the Richter   

What is the 95th percentile?   

(All answers to 3 decimal places.)

Solution

Mean ( u ) =1.184
Standard Deviation ( sd )=0.587
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 2) = (2-1.184)/0.587
= 0.816/0.587= 1.3901
= P ( Z <1.3901) From Standard Normal Table
= 0.9178                  
= 91.78 ~ 92% are Micro Earthquakes
b)
P(X > 3) = (3-1.184)/0.587
= 1.816/0.587 = 3.0937
= P ( Z >3.094) From Standard Normal Table
= 0.001                  
~ 0.10% are above 3

c)
P ( Z < x ) = 0.95
Value of z to the cumulative probability of 0.95 from normal table is 1.645
P( x-u/s.d < x - 1.184/0.587 ) = 0.95
That is, ( x - 1.184/0.587 ) = 1.64
--> x = 1.64 * 0.587 + 1.184 = 2.1496 ~ 2.15