Question

The mean and standard deviation of the tax value of all vehicles registered in

metro manila are 𝜇 = 𝑃ℎ𝑝 450 000 and 𝜎 = 𝑃ℎ𝑝 10000. Suppose random samples of 100 are drawn from the population of vehicles. Calculate the following:

a. mean of the sampling distribution

b. variance of the sampling distribution

b. standard deviation of the sampling distribution

Answer 1

a. mean of the sampling distribution

$$\mu_{\bar{X}}=450000$$

b. variance of the sampling distribution

$$Var_{\bar{X}}=\dfrac{\sigma^2}{ n}=\dfrac{10000^2}{ 100}=1000000$$

c. standard deviation of the sampling distribution

$$\sigma_{\bar{X}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10000}{\sqrt{100}}=1000$$