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For naturally occurring measurements Gauss showed that about 67% of observations will fall within 1 sigma, 95% within 2 sigma and 99.7% within 3 sigma. So if sigma is 0.2m and the average was 1.50m, I could bet on the next person to be between 1.3 and 1.7m nd my “conf d nc ” would b 67%. m co sm n, no known fo b ng o ly generous so I may decide to bet at 2 standard deviations and say that the next person will be between 1.1m and 1.9m. ow my “conf d nc ” go s up o 95%. f m s ll wo d, I could bet between 0.9m and 2.1m and now I would only be wrong 3 times in 1000 or 99.7% confident. Clearly with a critical estimate we would want a confident result. In theory it is not possible to obtain 100% confidence with the Gaussian model so we have set the limits somewhere. hssof n f do s“s ngh sgm l ls” ndh hgh h sgm l ls,h low h sk.
It should be noted that in nature nothing follows the Gaussian Model exactly. For example, we know that there are no people 3m high in the world so very low risk values are often ignored.
17.3 Probability in two dimensions
Something interesting happens when we try to guess two parameters at the same time and still need to be confident ofou s m s. ’ss yw nowgu ss h p son’sh gh nd h n llg nc . F s, s mpo n h w understand that these pa m s no “co l d”. no h wo ds,d sp wh you ll f ndsmgh lk o think, there is no relationship between height and intelligence. If we were measuring height and weight, we might xp c som “co l on” s nc ll p opl are probably going to be heavier than shorter people in general.
Watch what happens when we plot the normal distribution curves for the two parameters at once. In this diagram I have drawn the distribution curves on IQ for two height groups on either side of average height. Note that the average IQ for the small group is the same as the average IQ for the tall group. This demonstrates no correlation between height and intelligence. The average intelligence of all height groups remains the same.
Figure 71: Plotting two normal distribution curves at once.
Now we shall plot all the normal distributions for all the height groups.
hsnom lds bu on“moun n”d sc b s h probabilities of two parameters whose ranges are not h s m . Anyp ob bl y“con ou ”on h slop sof this mountain will therefore be elliptical in shape since the IQ range and the height range have different values.
Now we shall apply this to a section of wellbore. Let us imagine that the well section is straight and has an ncln on “” nd n zmuh “A” bu boh potentially in error.
Figure 72: Plotting where ranges are not the same
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