Answer :
Using the Central Limit Theorem, the correct option regarding the shape of the sample mean is given by:
d) The distribution of the sample mean is approximately normal by the central limit theorem.
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].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
For this problem, we have a skewed underlying distribution, however the sample size is greater than 30, hence the sampling distribution of sample means is normal and option d is correct.
More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
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