An opposition consists of 100 subjects, of which 5 are chosen randomly. To pass the test needs to be developed properly at least 3 of them. How many topics should be prepared for a security, at least 80% of the test will be overcome?
Consider the discrete random variable X = "number of items prepared from 5 randomly selected from a total of 100." Then X follows a distribution H (100, 5, m/100) or, in the terminology of R, H (m, 100-m, 5) being m the number of songs prepared.
then try to calculate such m to verify
P (X> = 3)> = 0.8, or whatever it is,
1-P (X <=2)> = 0.8 (*).
Making with R:
> m <-c(65,66,67,68,69,70)
> 1-phyper(2,m,100-m,5)
[1] 0.7696613 0.7851602 0.8002034 0.8147696 0.8288393 0.8423941
Es decir, que probamos con 5 valores de m y el menor valor entre ellos para el que se cumple la inecuación (*) es m = 67 temas .
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