Answer:
The shape is approximately normal, with mean of 140 grams and standard deviation of 5.37 grams.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
What is the shape of the distribution of the sample mean for all possible random samples of size 5 from this population?
By the Central Limit Theorem, the shape is approximately normal.
Mean is [tex]\mu = 140[/tex]
Standard deviation is [tex]s = \frac{12}{\sqrt{5}} = 5.37[/tex]
The shape is approximately normal, with mean of 140 grams and standard deviation of 5.37 grams.
