Answer:
The sampling distribution of the sample mean is approximately normal with mean 72 and standard deviation 1.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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.
Normally distributed with mean 72 and standard deviation 6.
This means that
A random sample of size 36
This means that
The sampling distribution of the sample mean is
By the Central Limit Theorem, it is approximately normal with mean 72 and standard deviation 1.