Q:

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18

Accepted Solution

A:
Answer:The mean and the standard error of the distribution of the sample mean are 200 and 2.Step-by-step explanation:Consider the provided information.Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18Sample size = n = 81Mean = ΞΌ=200Standard deviation = Οƒ = 18The mean of the distribution of the sample mean is same as the mean of the population. [tex]\mu_x=\mu=200[/tex]The standard error can be calculated as: [tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex]Substitute the respective values in the above formula.[tex]S.E.=\dfrac{18}{\sqrt{81}}=\dfrac{18}{9}=2[/tex]Hence, the mean and the standard error of the distribution of the sample mean are 200 and 2.