Assume that the Richter scale magnitudes of earthquakes are normally distributed

Question

Assume that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.103 and a standard deviation 0.543. Complete parts a through c below. a. Earthquakes with magnitudes less than 2.000 are considered "microearthquakes" that are not felt. What percentage of earthquake 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? Yes, because earthquakes above the 95th percentile are very rare and powerful. No, because not all earthquakes above the 95th percentile have magnitudes above 4.0. No, because no earthquakes above the 95th percentile have magnitudes above 4.0. Yes, because all earthquakes above the 95th percentile have magnitudes above 4.0.

Explanation / Answer

a) P(X < 2)

= P(z < (2 - 1.103)/0.543)

= P(z < 1.65)

= 0.9505

So,

The answer is 95.05%

b) P(X > 4)

= P(z > (4 - 1.103)/0.543)

= P(z > 5.335)

= 0

So,

The answer is 0%.

c) For 95th percentile, z = 1.645

Hence,

X = 1.103 + 1.645(0.543)

X = 1.996

So,

The 95th percentile is 1.996

d) Option B is correct.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---