This Question: 1 pt 7 of 25 (4 complete) This Test: 25 pts possible Assume that

Question

This Question: 1 pt 7 of 25 (4 complete) This Test: 25 pts possible Assume that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.087 and a standard deviation of 0.553. 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? (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? OA. No, because no earthquakes above the 95th percentile have magnitudes above 4.0. OB. No, because not all earthquakes above the 95th percentile have magnitudes above 4.0. O C. Yes, because earthquakes above the 95th percentile are very rare and powerful. O D. Yes, because all earthquakes above the 95th percentile have magnitudes above 4.0

Explanation / Answer

= 1.087

= 0.553
standardize x to z = (x - ) /
P(x < 2) = P( z < (2-1.087) / 0.553)
= P(z < 1.651) = 0.9506 (95.06 percent are "microearthquakes" )

(0.9506 come From normal probability table)

b.

= 1.087

= 0.553
standardize x to z = (x - ) /

P(x > 4) = P( z > (4-1.087) / 0.553)
= P(z > 5.26) =1-p(Z<5.26)=1-1=0.000 ..............0% percent will cause indoor items to shake)
c.

p(Z<z)=0.95

P(Z<1.645)=0.95

z=x-/

1.645=x-1.087/0.553

x=1.996

d) A. No, because not all earthquakes above the 95th percentile have magnitudes above 4.0.

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