Birthweights are distributed Normally, with a mean of 3.39kg and a standard deviation of 0.55kg. What is the probability that a randomly selected sample of 40 newborns will have an average weight of less than 3.45 kg?
Birthweights are distributed Normally, with a
What is the
Central Limit Theorem for mean:
If a random sample of size n is taken from a population having mean and standard deviation then, as the sample size increases, the sample mean approaches the normal distribution with mean and standard deviation σ/ sqrt(n).
By central limit theorem, the mean of the sampling distribution is μx-bar = 3.39.
The population standard deviation is, σ =0.55. The sample size is, n = 40.
The standard deviation using central limit theorem is σ/√n= 0.55/√40 = 0.08696.
Thus, the sampling distribution of the sample mean(x-bar) for sample of size 40 follows approximately normal distribution with mean μx-bar = 3.39 and standard deviation 0.08696.
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