Question

use the magnitudes, rounded to two decimal places, of the 100 earthquakes included in the accompanying data set to construct a frequency distribution. use a class wid 0.50 and begin with a lower class limit of 0.00. does the frequency distribution appear to be a normal distribution? click the icon to view the earthquake magnitudes. construct the frequency distribution. (type your answers as integers or decimals, rounded to the nearest hundredth as needed.)

Explanation:

Step1: Determine class intervals

Since the class width is \(0.50\) and the lower - class limit starts at \(0.00\), the class intervals are:
\(0.00 - 0.49\), \(0.50 - 0.99\), \(1.00 - 1.49\), \(1.50 - 1.99\), \(2.00 - 2.49\), \(2.50 - 2.99\)

Step2: Count frequencies for each class

• For the class \(0.00 - 0.49\):

Count the numbers in the data set that are \(\geq0.00\) and \(\lt0.50\). The values are \(0.39,0.22,0.00,0.39,0.29,0.23,0.39,0.11,0.29,0.39\). The frequency is \(10\)

• For the class \(0.50 - 0.99\):

Count the numbers \(\geq0.50\) and \(\lt1.00\). The values are \(0.71,0.74,0.64,0.69,0.64,0.89,0.65,0.98,0.78,0.78,0.85,0.92,0.98,0.64,0.69,0.74,0.64,0.69,0.93,0.79,0.78,0.85\). The frequency is \(22\)

• For the class \(1.00 - 1.49\):

Count the numbers \(\geq1.00\) and \(\lt1.50\). The values are \(1.01,1.23,1.66,1.32,1.01,1.25,1.61,1.81,1.28,1.34,0.92,1.01,1.01,1.49,1.43,1.01,1.24,1.42,1.34,0.92,1.28,1.01,1.25,1.42,1.34,0.93,1.43,1.24,1.48,1.42\). The frequency is \(30\)

• For the class \(1.50 - 1.99\):

Count the numbers \(\geq1.50\) and \(\lt2.00\). The values are \(1.75,1.57,1.54,1.57,1.63,1.82,1.56,1.77,1.64,1.31,1.78\). The frequency is \(11\)

• For the class \(2.00 - 2.49\):

Count the numbers \(\geq2.00\) and \(\lt2.50\). The values are \(2.19,1.99,2.23,2.46,2.21,1.98,2.24,2.47,2.24,2.47\). The frequency is \(10\)

• For the class \(2.50 - 2.99\):

Count the numbers \(\geq2.50\) and \(\lt3.00\). The value is \(2.96,2.92\). The frequency is \(2\)

Step3: Check for normal distribution

A normal distribution has a "bell - shaped" curve. In a frequency distribution for a normal distribution, the frequencies start low, increase to a maximum, and then decrease. Here, the frequencies first increase (\(10,22,30\)) and then decrease (\(11,10,2\))

Answer:

Magnitude	Frequency
\(0.50 - 0.99\)	\(22\)
\(1.00 - 1.49\)	\(30\)
\(1.50 - 1.99\)	\(11\)
\(2.00 - 2.49\)	\(10\)
\(2.50 - 2.99\)	\(2\)

The frequency distribution appears to be a normal distribution.