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A simple random sample of size n=53 is obtained from a population with μ=53 and σ=7. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally​ distributed? Why? What is the sampling distribution of x​?

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Answer:

No, because the Central Limit Theorem posits that regardless of the shape of the underlying​ population, the sampling distribution of bar x becomes approximately normal as the sample​ size (n) increases.

The sampling distribution of x is;


\mu_(\overline x) = \mu = 53

Explanation:

Given that:

The sample size n = 53

The population mean μ = 53

The standard deviation σ = 7

The sampling distribution of x is;


\mu_(\overline x) = \mu = 53

Sampling distribution of the standard deviation is:


\sigma _x =(\sigma)/(√(n))


\sigma _x =(7)/(√(53))


\sigma _x =(7)/(7.28)


\sigma _x =0.96

User Tom Xue
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