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Sagot :
Answer:
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours
This means that [tex]\mu = 945, \sigma = 21[/tex].
What is the approximate standard deviation of the sampling distribution of the mean for all samples of size n?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
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