Fission tracks are trails found in uranium-bearing minerals, left by fragments released during fission events. The article "Yo-yo Tectonics of the Nigde Massif During Wrenching in Central Anatolia" (D. Whitney, P. Umhoefer, et al., Turkish Journal of Earth Sciences, 2008:209-217) reports that fifteen tracks on one rock specimen had an average track length of 13 µm with a standard deviation of 2 µm.

Assuming this to be a random sample from an approximately normal population, find a 99% confidence interval for the mean track length for this rock specimen.

Answer: = (11.67, 14.33) µm

Therefore at 99% confidence interval (a, b) = (11.67, 14.33) µm

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean track length x = 13 µm

Standard deviation r = 2 µm

Number of samples n = 15

Confidence interval = 99%

z (at 99% confidence) = 2.58

Substituting the values we have;

13+/-2.58 (2/√15)

13+/-2.58 (0.516397779494)

13+/-1.33

= (11.67, 14.33) µm

Therefore at 99% confidence interval (a, b) = (11.67, 14.33) µm