Question

Question 41 2.381 points Save Answer Random samples of size 49 are taken from a population that has 200 elements, a mean of 100, and a variance of 196. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are 100 and 28 100 and 2 100 and 24.39 100 and 1.74

Answer 1

We know that If X is a random variable having mean $\mu$ and standard deviation $\sigma$, let x1, x2, x3, xn....... be the random sample taken from X then the distribution of sample mean X bar follows Normal distribution with mean $\mu$ and standard deviation

$\sigma$/$\sqrt(n)$

We have given mean $\mu$ = 100 , variance $\sigma$² = 196 hence we get standard deviation $\sigma$ = sqrt(196) = 14

and sample size n = 49

Hence we get the mean of sample distribution of sample mean is $\mu$ = 100

and Standard error of sample distribution of sample mean is = $\sigma/sqrt(n)$ = 14 / 7 = 2

Hence we get   the mean and standard error of sample distribution of sample mean is 100 and 2

Hope this will help you. Thank you :)