# Statistics normal distribution

Statistics normal distribution

Ex. 22 Richter scale earthquake magnitudes are listed in Data Set 16 of Appendix B.

a. Determine whether those magnitudes are from a population with a normal distribution

b. For the Richter scale, assume that the magnitude of the energy from an earthquake is first measured, then the logarithm (base 10) of the value is computed. Based on this description of the Richter scale and the resule from part (a), what is the distribution of the original measurements before their logarithms are computed?

c. Given that the magnitudes in Data Set 16 result from computing logarithms (base 10), construct the normal quantile plot of the original magnitudes before logarithms are applied. Do the original values appear to be from a population with a normal distribution?

MAG     DEPTH

0.70      6.6

0.74      2.0

0.64      15.3

0.39      17.2

0.70      3.2

2.20      2.2

1.98      14.8

0.64      5.6

1.22      6.1

0.20      9.1

1.64      18.5

1.32      8.1

2.95      10.0

0.90      13.7

1.76      8.0

1.01      7.0

1.26      18.6

0.00      8.2

0.65      5.7

1.46      18.9

1.62      13.7

1.83      4.5

0.99      8.3

1.56      6.0

0.40      14.2

1.28      5.4

0.83      17.7

1.34      9.9

0.54      17.3

1.25      5.1

0.92      5.3

1.00      15.9

0.79      13.7

0.79      4.2

1.44      5.7

1.00      5.9

2.24      15.1

2.50      8.5

1.79      14.7

1.25      16.4

1.49      4.7

0.84      8.6

1.42      8.2

1.00      15.2

1.25      10.1

1.42      14.5

1.35      5.2

0.93      7.9

0.40      3.3

1.39      6.4