# Mathematics - Finite Mathematics

My question is as follows:

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.

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#### 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.