Consider the following discrete population distribution:
We randomly draw samples of size 5 from this population using the simple random sampling technique.If we know that μx = 5.4, σx= 2.069, what are the mean and the standard deviation of the sampling distribution of sample means? Assume the Central Limit Theorem applies.
A) μ = 5.4, σ = 2.069
B) μ = 1.08, σ = 0.4138
C) μ = 5.4, σ = 0.9253
D) μ = 5.4, σ = 0.4138

Question

Consider the following discrete population distribution: ​  ​
We randomly draw samples of size 5 from this population using the simple random sampling technique.If we know that μx = 5.4, σx= 2.069, what are the mean and the standard deviation of the sampling distribution of sample means? Assume the Central Limit Theorem applies.
A) μ = 5.4, σ = 2.069 
B) μ = 1.08, σ = 0.4138 
C) μ = 5.4, σ = 0.9253 
D) μ = 5.4, σ = 0.4138

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of sample means is normally distributed with a mean equal to the population mean (μx) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σx/sqrt(n)). Therefore, the mean of the sampling distribution of sample means is 5.4 and the standard deviation is 2.069/sqrt(5) = 0.9253. Option C is the only choice that matches both of these values.

Consider the Following Discrete Population Distribution: ​ ​

Consider the Following Discrete Population Distribution: