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Sagot :
Answer:
By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
Sample mean was $6,425 with a standard deviation of $3,156
This means that [tex]\mu = 6425, \sigma = 3156[/tex]
Sample of 84:
This means that [tex]n = 84, s = \frac{3156}{\sqrt{84}} = 344.35[/tex]
a. Which distribution should you use for this problem?
By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.
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