A population has a mean muμequals=130130 and a standard deviation sigmaσequals=3030. Find the mean and standard deviation of the sampling distribution of sample means with sample size nequals=5151.

Mean 130

Standard deviation 4.2

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , the sample means with size n of at least 30 can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

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