The magnitude of earthquakes since 1902 measure 0.1 or higher on the Richter sca

Question

The magnitude of earthquakes since 1902 measure 0.1 or higher on the Richter scale in Arizona is approximately normally distributed, with m=6.2, and s=0.5 according to data obtained from U.S.G.S. A) In 2011, an earthquake in Pheonix, AZ has a magnitude of 7.2. What is the probability that a randomly selected earthquake in AZ has a magnitude of 7.2 or higher? B) What is the probability that a randomly selected earthquake in AZ has a magnitude between 5.4 and 7.2. C) In 1911, the great Tucson earthquake had a magnitude of 8.25. What is the probability that a randomly selected earthquake in AZ has a magnitude of 8.25 or higher? D) What is the percentile rank of a AZ earthquake that measures 5.4 on the Richter scale? E) Determine the magnitude of earthquakes in AZ that make up for the middle 90% of magnitudes.
The magnitude of earthquakes since 1902 measure 0.1 or higher on the Richter scale in Arizona is approximately normally distributed, with m=6.2, and s=0.5 according to data obtained from U.S.G.S. A) In 2011, an earthquake in Pheonix, AZ has a magnitude of 7.2. What is the probability that a randomly selected earthquake in AZ has a magnitude of 7.2 or higher? B) What is the probability that a randomly selected earthquake in AZ has a magnitude between 5.4 and 7.2. C) In 1911, the great Tucson earthquake had a magnitude of 8.25. What is the probability that a randomly selected earthquake in AZ has a magnitude of 8.25 or higher? D) What is the percentile rank of a AZ earthquake that measures 5.4 on the Richter scale? E) Determine the magnitude of earthquakes in AZ that make up for the middle 90% of magnitudes.
A) In 2011, an earthquake in Pheonix, AZ has a magnitude of 7.2. What is the probability that a randomly selected earthquake in AZ has a magnitude of 7.2 or higher? B) What is the probability that a randomly selected earthquake in AZ has a magnitude between 5.4 and 7.2. C) In 1911, the great Tucson earthquake had a magnitude of 8.25. What is the probability that a randomly selected earthquake in AZ has a magnitude of 8.25 or higher? D) What is the percentile rank of a AZ earthquake that measures 5.4 on the Richter scale? E) Determine the magnitude of earthquakes in AZ that make up for the middle 90% of magnitudes.

Explanation / Answer

a)

P( z > 7.2-6.2 / 0.5 )

P( z >2 ) = 0.0228

b)

P( 5.4 - 6.2 / 0.5 < z < 7.2 - 6.2 / 0.5 )

P( -1.6 < z < 2 ) = 1 - 0.0548 - 0.0228 = 0.9224

c)

P( z > 8.25 - 6.2 / 0.5 )

P( z >4.1 ) = 0.000001

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