Stat141 Oct18    (part B)
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normal approximation to discrete distrib. via continuity correction SW 4.5
litter size mice example table 4.1  mean 7.8, sd 2.3
> #SW p.138, ladder of transformations log(lentil)
> #SW sec 4.5 litter size example
> #prob Y in [5,10] actual discrete and normal approx
> pnorm(10, 7.8, 2.3) - pnorm(5, 7.8, 2.3)
[1] 0.718868
> #much smaller than actual population relative frequency .808 SW p.142
> pnorm(10.5, 7.8, 2.3) - pnorm(4.5, 7.8, 2.3) #using continuity correction
[1] 0.8041105
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> #normal approx to binomial, clutch failures n=100, pi = .1 approx N(10,3)
> pbinom(9, 100, .1)
[1] 0.4512902
> pnorm(9,10,3); pnorm(9.5, 10,3)
[1] 0.3694413
[1] 0.4338162
# continuity correction considerably improves approximation