Suppose that you are given a simple chain of length N beads, and in this chain you tie one knot in the centre. You perform an experiment 25 times in which each time you place the chain on a vibrating plate and measure how long it takes to unknot and you make a list of the un-knotting times as follows:
chain1 = {5.50, 8.10, 4.65, 4.03, 14.04, 9.94, 10.34, 3.47, 5.19,
8.54, 5.63, 5.53, 5.38, 3.44, 4.32, 12.69, 5.66, 2.34, 14.72, 5.07,
5.90, 6.60, 4.75, 5.59, 4.85}

From this we calculated the mean un-knotting time is: 6.6508, with standard deviation 3.2977.

My question is how can one find the probability based on the data above of finding the knot still knotted (i.e., still "alive") at time t.

Solution Preview

m = 6.6508, s = 3.2977, n = 25

Standard Error of the mean unknotting time = s/ sqrt n = 3.2977/ sqrt 25 = 0.6595

We want to find the probability that the knot is still knotted at time ...

Solution Summary

A complete, neat and step-by-step solution that calculates the mean unknotting time.

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