Answer:
The standard deviation of the distribution of sample proportions is 0.0229.
Explanation:
Central Limit Theorem
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
and standard deviation
70% of all city residents support the tax increase to build a combined bus and train station.
This means that
400 city residents
This means that
What is the standard deviation of the distribution of sample proportions?
By the Central Limit Theorem:
The standard deviation of the distribution of sample proportions is 0.0229.