Answer:
Mean 130
Standard deviation 4.2
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n of at least 30 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, we have that:
[tex]\mu = 130, \sigma = 30[/tex]
Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 51.
By the Central Limit Theorem,
Mean is 130
Standard deviation [tex]s = \frac{30}{\sqrt{51}} = 4.2[/tex]
