Statistics for Environmental Engineers

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r


Pr(x < r) = F(r: n,p) = У n-    px( 1 —p)n-x


x!(n —x)!


Table 19.2, calculated from this equation, gives the cumulative probability of x successes in n = 20 trials for several values of p. Table 19.3, which gives the probability of exactly x occurrences for the same


Probability of Observing Exactly x Successes in 20 Trials, where p is the True Random Probability of Success in a Single Trial


x


p = 0.05


0.10


0.15


0.20


0.25


0.50


0


0.36


0.12


0.04


0.01




1


0.38


0.27


0.14


0.06


0.02



2


0.18


0.29


0.22


0.14


0.07



3


0.06


0.19


0.25


0.20


0.14



4


0.02


0.09


0.18


0.22


0.18


0.01


5


0.03


0.10


0.17


0.21


0.01


6


0.01


0.05


0.11


0.17


0.04


7


0.01


0.06


0.11


0.07


8


0.01


0.02


0.06


0.12


9


0.01


0.02


0.16


10


0.01


0.18


11


0.16


12


0.12

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