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Sagot :
Using the Central Limit Theorem, it is found that the mean of the sampling distribution is of 78 and the standard deviation is of 2.84.
What does the Central Limit Theorem state?
It states 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].
In this problem, for the population, we have that [tex]\mu = 78, \sigma = 11[/tex].
Then, considering samples of n = 15, we have that the standard deviation is given by:
[tex]s = \frac{11}{\sqrt{15}} = 2.84[/tex].
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
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