Question

A population has μ = 80 and a standard deviation of σ = 5.2. What are the mean and standard deviation of the sampling distribution X if a sample of 100 were taken?

A) μ = 80, σ = 0.52.
B) μ = 80, σ = 0.052.
C) μ = 80, σ = 5.2.
D) μ = 80, σ = 52.
E) μ = 80, σ = 520.

Answer 1

The mean and standard deviation of the sampling distribution can be calculated using specific formulas. In this case, the mean is 80 and the standard deviation is 0.52 (option A).

Step-by-step explanation:

The mean and standard deviation of the sampling distribution of a population can be calculated using the following formulas:

Mean of sampling distribution (μx) = Population mean (μ)

Standard deviation of sampling distribution (σx) = Population standard deviation (σ) / Square root of sample size (n)

In this case, the population mean (μ) is given as 80 and the population standard deviation (σ) is given as 5.2. The sample size (n) is 100.

Calculating the mean of the sampling distribution:

μx = 80

Calculating the standard deviation of the sampling distribution:

σx = 5.2 / sqrt(100) = 0.52

Therefore, the mean (μ) of the sampling distribution is 80 and the standard deviation (σ) is 0.52 (option A).