Assume that the Richter scale magnitudes of earthquakes are normally distributed
ID: 3225889 • Letter: A
Question
Assume that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.022 and a standard deviation of 0.579. Complete parts a through c below. a. Earthquakes with magnitudes less than 2.000 are considered "microearthquakes" that are not felt. What percentage of earthquakes fall into this category? 95.44% (Round to two decimal places as needed.) b. Earthquakes above 4.0 will cause indoor items to shake. What percentage of earthquakes fall into this category? % (Round to two decimal places as needed.) c. Find the 95th percentile. (Round to three decimal places as needed.) Will all earthquakes above the 95th percentile cause indoor items to shake? A. No, because no earthquakes above the 95th percentile have magnitudes above 4.0. B. Yes, because earthquakes above the 95th percentile are very rare and powerful. C. Yes, because all earthquakes above the 95th percentile have magnitudes above 4.0. D. No, because not all earthquakes above the 95th percentile have magnitudes above 4.0.Explanation / Answer
Mean = 1.022
Standard deviation = 0.579
a) Probability of earthquakes of magnitude less than 2 = P(X < 2)
= P(Z < (2-mean)/standard deviation)
= P(Z < (2-1.022)/0.579)
= P(Z < 1.69)
= 0.9545 = 95.45%
b) P(X>4) = 1 - P(X <4)
= 1 - P(Z < (4-1.022)/0.579)
= 1 - P(Z < 5.14)
= 1 - 1
= 0.00%
c) 95th percentile is when P(X < a) = 0.95
P(Z < (a - 1.022)/0.579) = 0.95
(a - 1.022)/0.579) = 1.645
a = 1.974
95th percentile = 1.974
d) No, because not all earthquakes above the 95th percentile have magnitude above 4