Answer:
The mean of the sampling distribution of the proportion of employees who wear contact lenses is 0.12 and the standard deviation is 0.0145.
Step-by-step 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
12% of the employees wear contact lenses.
This means that
Samples of 500:
This means that
What are the mean and standard deviation of the sampling distribution of the proportion of employees who wear contact lenses?
Mean:
Standard deviation:
The mean of the sampling distribution of the proportion of employees who wear contact lenses is 0.12 and the standard deviation is 0.0145.