Question

The magnitude of earthquakes since 1900 that measure 0.1 or higher on the Richter Scale in California is approximately normally distributed with µ = 6.2 and o =0.5, according to the data obtained from the U.S. Geological Survey. based on this data, geologists can tell us that approximately 20% of all earthquakes in California have magnitudes of ? or more.

Answer 1

Solution:
Given in the question
The magnitude of earthquakes since 1900 that measure 0.1 or higher on the Richter Scale in California is approximately normally distributed with
Mean() = 6.2
Standard deviation() = 0.5
we need to calculate that approximately 20% of all earthquakes in California have magnitudes of ? or more
So P-value = 0.8
From Z table we found Z-score = 0.84162
So Earthquakes in California magnitude can be calculated as
X = + Z-score * = 6.2 + 0.84162*0.5 = 6.2 + 0.42 = 6.62
P(X>6.62) = 0.20
Based on this data, geologists can tell us that approximately 20% of all earthquakes in California have magnitudes of 6.62 or more