A particular nuclear plant releases a detectable amount of radioactive gases twice a month on the average. Find the probability that there will be at most four such emissions during a month. What is the expected number of emissions during a three-month period? If, in fact, 12 or more emissions are detected during a three-month period, do you think that there is a reason to suspect the reported average figure of twice a month? Explain, on the basis of the probability involved.
a. Geophysicists determine the age of a zircon by counting the number of uranium fission tracks on a polished surface. A particular zircon is of such an age that the average number of tracks per square centimeter is five. What is the probability that a 2-cm sample of this zircon will reveal at most three tracks thus leading to an underestimation of the age of the material?