m*****e
发帖数: 207 | 1 use normal approximation
let X be the number of sixes, X ~ Bin(360, 1/6)
E[X] = 60, Var[X] = 50.
then Z = (X-60)/sqrt(50) ~ N(0,1), approximately
. .
Pr(X>=70) = Pr(X>=69.5) = Pr(Z>=1.3435) = 0.0896
the exact number is 0.0914 | m*****e
发帖数: 207 | 2
If no calculator is allowed, then use the 68-95-99.7 rule.
1.3435 is between 1 and 2 sd, so the corresponding quantile
shd be between 84% and 97.5%.
hence the probability is between .025 and .16 QED
【在 m*****e 的大作中提到】
: use normal approximation
: let X be the number of sixes, X ~ Bin(360, 1/6)
: E[X] = 60, Var[X] = 50.
: then Z = (X-60)/sqrt(50) ~ N(0,1), approximately
: . .
: Pr(X>=70) = Pr(X>=69.5) = Pr(Z>=1.3435) = 0.0896
: the exact number is 0.0914
|
|
