Question

Assume that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.026 and a standard deviation of 0.504. Complete parts a through c below. a. Earthquakes with magnitudes less than 2.000 are considered "microearthquakes that are not folt. what percentage of earthquakes fall into this category? (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? O A. Yes, because earthquakes above the 95th percentile are very rare and powerful OB. Yes, because all earthquakes above the 95th percentile have magnitudes above 4.0. OC. No, because not all earthquakes above the 95th percentile have magnitudes above 4.0. OD. No, because no earthquakes above the 95th percentile have magnitudes above 4.0. Hide Stop sharing Click to select your answers) Il autoproctoru.com is sharing your screen

Answer 1

'le. 2000 category 6 The Richter scale magnitudes of earthquates (x) are normally distributed N(U11026, 6= 0.504) a) Earthquakes with magnitudes dess than are considered micro-earth quakes. The percent of earth qualces falls in this are given by P(X<2.0)=P(tae 21000 -7.026 0.–1026) 0.504 Plze 0.974 0.504. = P(Z 3 1.93) P(x32.000) = 0.9732 table. ... 97.32% earth quales falls in this Category. will cause indoor b) Earthquakes above 410 items to shake, the percentage of earthquake falls in this category given by: P(x>40) Fl- P(x 3400 #by using a

P(*34,0)=1* PLZ€ 400-10026 0.504 El-P(?< 21974 ;) 0.504 - P(Z < 5.90) -1-O.gggggg71 by using walio Cop(x>4.0) e o e table P(Z < 500) = 0.99999921 0% of earthquakes fall into this Category. C. The g5 Yoth percentile is P(xsn=0.95 il p(x-year 1-026) = 0.95 0.504 P(Z < N-1.026. ) = orgs 0.504 2-10 26 0504 =Z0.95 by using z table » . z 2-1.026 1.64 0504 Z095=1064 => x= 1.640.504 + 1.026 = 1.853 --2-1853
Not all earthquakes above the 95th percentile cause indoor items to shake since:

C. No, because not all earthquakes above the 95th percentile have magnitude above 4.0.