Answer to Question #322891 in Statistics and Probability for Nate

Question

B. Find the mean (𝝁) variance (𝝈 2)and standard deviation (𝝈) of the population given the sample size, and the means and variances of the sampling distribution of the means. Sample size n were randomly selected from the population

4. 𝑛 = 5

𝜇𝑥 = 3

𝜎²𝑥 = 4.5

Mean:

Variance:

Standard Deviation:

5. 𝑛 = 7

𝜇𝑥 = 10

𝜎²𝑥 = 6

Mean:

Variance:

Standard Deviation:

Answer 1

Mean of the population is equal to the mean of the sampling distribution, variance is equal to sample distribution variance multiplied by n. So,

1) $\mu=\mu_x=3$

$\sigma^2=\sigma^2_x*5=4.5*5=22.5$

$\sigma=\sqrt{\sigma}=\sqrt{22.5}\approx4.74$

2) $\mu=\mu_x=10$

$\sigma^2=\sigma^2_x*7=6*7=42$

$\sigma=\sqrt{\sigma}=\sqrt{42}\approx6.48$