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Pani-rosa [81]
3 years ago
15

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 dis

tributed for the sampling distribution of x to be approximately normally​ distributed? Why? What is the sampling distribution of x​?
Mathematics
1 answer:
Y_Kistochka [10]3 years ago
4 0

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

Step-by-step 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 =\dfrac{\sigma}{\sqrt{n}}

\sigma _x =\dfrac{7}{\sqrt{53}}

\sigma _x =\dfrac{7}{7.28}

\sigma _x =0.96

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