poisson / normal distribution ?

[匿名]

2017-11-28 8:50 pm

Given a ranodm sample of X1 , X2 .... X40 which is drawn from population with poisson distribution 3.5 . Find the probability that the sample mean is between 3.4 and 4.3 ...
Which method should i use here ? Normal or poisson distribution ?

回答 (1)

cidyah

2017-11-28 9:23 pm

✔ 最佳答案

Sample mean has a Poisson distribution with mean 3.5 and variance 3.5
mean = variance
sd = sqrt(3.5) = 1.8708
You have to use normal distribution because you want to compute the probability that the mean is between 3.4 and 4.3

Mean μ = 3.5
Standard deviation σ = 1.8708
Standard error σ / √ n = 1.8708 / √ 40 = 0.2957995
standardize xbar to z = (xbar - μ) / (σ / √ n )
P( 3.4 < xbar < 4.3) = P[( 3.4 - 3.5) / 0.295799 < z < ( 4.3 - 3.5) / 0.295799]
P( -0.3381 < z < 2.7045) = P( z < 2.7045) - P( z < -0.3381) = 0.9965 - 0.3669 = 0.6296
(from normal probability table)

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