The following data set lists 50 magnitudes Richter scale of

The following data set lists 50 magnitudes (Richter scale) of 50 earthquakes, and those earthquakes have magnitudes with a standard deviation of

0.587. 0.70 2.20 1.64 1.01 1.62 1.28 0.92 1.00 1.49 1.42 0.74 1.98 1.32 1.26 1.83 0.83 1.00 2.24 0.84 1.35 0.64 0.64 2.95 0.00 0.99 1.34 0.79 2.50 1.42 0.93 0.39 1.22 0.90 0.65 1.56 0.54 0.79 1.79 1.00 0.40 0.70 0.20 1.76 1.46 0.40 1.25 1.44 1.25 1.25 1.39

Convert the magnitude of the strongest earthquake to a score.

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    59.797      
As n =    51      
Thus,          
X =    1.172490196      
          
Setting up tables,          
x   x - X   (x - X)^2  
0.587   -0.585490196   0.34279877  
0.7   -0.472490196   0.223246985  
2.2   1.027509804   1.055776397  
1.64   0.467509804   0.218565417  
1.01   -0.162490196   0.026403064  
1.62   0.447509804   0.200265025  
1.28   0.107509804   0.011558358  
0.92   -0.252490196   0.063751299  
1   -0.172490196   0.029752868  
1.49   0.317509804   0.100812476  
1.42   0.247509804   0.061261103  
0.74   -0.432490196   0.18704777  
1.98   0.807509804   0.652072083  
1.32   0.147509804   0.021759142  
1.26   0.087509804   0.007657966  
1.83   0.657509804   0.432319142  
0.83   -0.342490196   0.117299534  
1   -0.172490196   0.029752868  
2.24   1.067509804   1.139577181  
0.84   -0.332490196   0.11054973  
1.35   0.177509804   0.03150973  
0.64   -0.532490196   0.283545809  
0.64   -0.532490196   0.283545809  
2.95   1.777509804   3.159541103  
0   -1.172490196   1.37473326  
0.99   -0.182490196   0.033302672  
1.34   0.167509804   0.028059534  
0.79   -0.382490196   0.14629875  
2.5   1.327509804   1.76228228  
1.42   0.247509804   0.061261103  
0.93   -0.242490196   0.058801495  
0.39   -0.782490196   0.612290907  
1.22   0.047509804   0.002257181  
0.9   -0.272490196   0.074250907  
0.65   -0.522490196   0.272996005  
1.56   0.387509804   0.150163848  
0.54   -0.632490196   0.400043848  
0.79   -0.382490196   0.14629875  
1.79   0.617509804   0.381318358  
1   -0.172490196   0.029752868  
0.4   -0.772490196   0.596741103  
0.7   -0.472490196   0.223246985  
0.2   -0.972490196   0.945737181  
1.76   0.587509804   0.34516777  
1.46   0.287509804   0.082661887  
0.4   -0.772490196   0.596741103  
1.25   0.077509804   0.00600777  
1.44   0.267509804   0.071561495  
1.25   0.077509804   0.00600777  
1.25   0.077509804   0.00600777  
1.39   0.217509804   0.047310515  
          
Thus, Sum(x - X)^2 =    17.25167275      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    51      
          
s^2 =    0.345033455      
          
Thus,          
          
s =    0.587395484      

Thus, as the highest score is x = 2.95, then

z = (x - X)/s = (2.95 - 1.172490196)/0.587395484

z = 3.026086942 [ANSWER]