Answer:
By the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.4 years.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
The mean for the entire population is 5.4 years.
So, by the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.4 years.