Normal distribution 1
2009-07-18 12:34 am
Twenty unbiased coins are tossed and the number of heads counted. This experiment is repeated 1000 times. Use the normal distribution as an approximation to the binomial distribution to calculate the number of times eight or more heads are to be expected.
回答 (1)
2009-07-18 4:48 am
✔ 最佳答案
Let X be the random variable of number of heads got.X ~ B(20 , 0.5)
Under normal approximation to binomial distribution.
X ~ N(20 X 0.5 , 20 X 0.5 X (1 - 0.5))
X ~ N(10 , 5)
P(X >= 8)
= P[z >= (8 - 0.5 - 10)/sqrt5]
= P(z >= -1.118033989)
= 0.5 + 0.3682
= 0.8682
So, the expected number of times eight or more heads got
= 1000 X 0.8682
= 868 times
參考: Physics king
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