z Scores. In Exercises, express allz scores with two decimal places.

Earthquakes Data Set 16 in Appendix B lists 50 magnitudes (Richter scale) of 50 earthquakes, and those earthquakes have magnitudes with a mean of 1.184 with a standard deviation of 0.587. The strongest of those earthquakes had a magnitude of 2.95.

a. What is the difference between the magnitude of the strongest earthquake and the mean magnitude?

b. How many standard deviations is that (the difference found in part (a))?

c. Convert the magnitude of the strongest earthquake to a z score.

d. If we consider “usual” magnitudes to be those that convert to z scores between −2 and 2, is the magnitude of the strongest earthquake usual or unusual?

Answer

Step 1 of 4</p>

a)The difference between the magnitude of the strongest earthquake and the mean magnitude is

2.95-1.184=1.766

Step 2 of 4</p>

b) How many standard deviations is

(2.95-1.184)/0.587=3.009