Again with this nonsense. The curve is not Gaussian, it cannot be Gaussian. It must be truncated. The probability quickly drops to zero.
Well, Machiavelli's point has some (very limited, and misunderstood) validity.
The experimental curve for t(lag) is demonstrably a modified bell curve, with a significantly squashed left hand side (owing to the fact that the curve cannot extend beyond t=0) and a shortened tail on the right hand side (owing to the fact that there is a definitive upper limit to t(lag)).
And Machiavelli is correct to say that we are dealing with the far right hand side of this bell curve, where there is (by definition) a shallower gradient, and where therefore there is a lesser step change in probability per unit of time than for the steep middle part of the curve.
But....... the curve at this point still enables cogent, statistically-valid analysis. I can go over the precise data at some point if necessary, but from memory, the curve obeys the following approximate properties:
At t=150, the area under the curve to the right of this point equates to about 2%, meaning that there's a 2% probability that t(lag) is >= 150 minutes.
At t=180, the area under the curve to the right equates to about 0.2%, meaning that a) there's a 2% probability that t(lag) is >=180m, and b) there's a 1.8% (2%-0.2%) probability that t(lag) is between 150m and 180m.
At t=210, the area under the curve to the right equates to about 0.01%, meaning that a) there's a 0.01% probability that t(lag) is >=210m, b) there's a 1.99% (2%-0.01%) probability that t(lag) is between 150m and 210m.
At t=240, the curve has reached zero on the y-axis, showing that there's zero probability of t(lag) >=240m.
Now, with all those in mind, the pertinent questions are actually conditional probability calculations. These are as follows:
Q1: Given that t >=150*, what is the probability that t(lag) is between 150-180m as opposed to >180m?
A1: 90%. In other words, it's 90% likely that Kercher died between 9pm and 9.30pm as opposed to later than 9.30pm.
Q2: Given that t >=150, what is the probability that t(lag) is between 150-210m as opposed to >210m?
A2: 99.5%. In other words, it's 99.5% likely that Kercher died between 9pm and 10pm as opposed to later than 10pm.
Q3: Given that t >=150, what is the probability that t(lag) is between 150-240m as opposed to >240m?
A3: 100%. It's a statistical certainty that Kercher died between 9pm and 10.30pm as opposed to later than 10.30pm.
That's what an analysis of the statistics, and the proper application of conditional probability theory, tell us. I will concede that there's bound to be some margin of error around these numbers, but the overall message will remain absolutely firm:
it's very highly likely that Kercher died between 9pm and 9.30pm; it's a virtual certainty that she died between 9pm and 10pm, and its a total certainty that she died before 10.30pm.
* Working on the knowledge that start of Kercher's last meal (which is the relevant starting point here) took place at around 6.30pm, and that she was last knowingly alive just before 9pm (150 minutes later)