Paleomagnetic studies of Canadian volcanic rock known as the Carmacks Group have recently been completed. The studies revealed that the northward displacement of the rock units has an approximately normal distribution with standard deviation of 500 kilometers (Canadian Journal of Earth Sciences, Vol. 27, 1990). One group of researchers estimated the mean displacement at 1,500 kilometers, whereas a second group estimated the mean at 1,200 kilometers.

a. Assuming the mean is 1,500 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

b. Assuming the mean is 1,200 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

c. If, in fact, the northward displacement is less than 500 kilometers, which is the more plausible mean, 1,200 or 1,500 kilometers?