Machine Learning Problem

Page Title

Suppose the underlying population of elements is N(4,16) and one element from this population is selected. We want to find the probability that the selected element has a value less than 3.0 or greater than 6.1. In solving this problem, the relevant distribution is specified: x is N(4,16). The probability of observing x<3.0 in the distribution of x is equivalent to the probability of observing z<(3.0−4)/4=−0.25 in the standard Gaussian distribution. Going to Table 1-2, z=0.25 is approximately the 60th percentile of the standard Gaussian distribution and by symmetry z=−0.25 is approximately the 40th percentile. Thus, the probability of observing a z value less than or equal to −0.25 is approximately 0.40. The probability of observing x>6.1 is equivalent to the probability of observing z>(6.1−4)/(4)=+0.525. Table 1-2 gives the probability of observing a z<0.525 as approximately 0.70, so the probability of observing a z<0.525 approximately equals 1−0.70 or 0.30. The desired probability of observing a sample observation less than 3.0 or greater than 6.1 is the sum of 0.40 and 0.30, which is approximately 0.7 or 7 chances in 10.

[TUTORIAL] ➡️ Gaussian distribution