The magnitude of earthquakes since 1950 measure 0.1 or higher on the Richter sca

Question

The magnitude of earthquakes since 1950 measure 0.1 or higher on the Richter scale. Arizona is approximately normally distributed, with m=6.2 and s=0.5. A) What is the percentile rank of an AZ earthquake that measures 5.4 on the Richter scale? B) Determine the magnitude of earthquakes in AZ that make up the middle 90% of magnitudes. The magnitude of earthquakes since 1950 measure 0.1 or higher on the Richter scale. Arizona is approximately normally distributed, with m=6.2 and s=0.5. A) What is the percentile rank of an AZ earthquake that measures 5.4 on the Richter scale? B) Determine the magnitude of earthquakes in AZ that make up the middle 90% of magnitudes. A) What is the percentile rank of an AZ earthquake that measures 5.4 on the Richter scale? B) Determine the magnitude of earthquakes in AZ that make up the middle 90% of magnitudes.

Explanation / Answer

the mean = 6.2

standard deviation = 0.5

as the distribution is normally distributed therefore we will use the formula for

z score = (x-mean)/standard devitaion

a) x = 5.4

z score = (5.4-6.2)/0.5 = -1.6

hence the value of -1.6 will be taken from the z table which comes out to be = 0.0548

hence percentile = 5.48 percentile

b) x = mean + z* standard deviation

z score for 90% = 1.645

hence the x = 6.2+1.645*0.5 = 7.0225

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