Questions: Can a normal approximation be used for a sampling distribution of sample means from a population with μ=56 and σ=10, when n=9?

Can a normal approximation be used for a sampling distribution of sample means from a population with μ=56 and σ=10, when n=9?
Transcript text: Can a normal approximation be used for a sampling distribution of sample means from a population with $\mu=56$ and $\sigma=10$, when $n=9$ ?
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Solution

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Solution Steps

Step 1: Check Sample Size

The sample size is 9, which is less than 30. According to the Central Limit Theorem (CLT), if the sample size is less than 30, the sampling distribution of the sample mean might not be approximately normally distributed unless the population distribution is approximately normal.

Step 2: Conclusion

Since the sample size does not meet the criteria set by the CLT for a large enough sample size, a normal approximation might not be suitable for the sampling distribution of sample means without further information about the population distribution.

Final Answer:

A normal approximation ^cannot^ be used for the sampling distribution of sample means without further information on the population distribution's shape.

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