Answer to Question #184550 in Statistics and Probability for Kapsy

Question

Let the population be given by the numbers. Take all random samples of size 3 without replacement and obtain the sampling distribution of the sample mean

Answer 1

Let the population consists of numbers $15,9,24,6$ and $18$ .

Sampling distribution of size 3 can be given as

Sampling distribution of Sample mean,

$P(\bar X = 16) = \dfrac{3}{10}$

$P(\bar X = 15) = \dfrac{1}{10}$

$P(\bar X = 19) = \dfrac{3}{10}$

$P(\bar X = 13) = \dfrac{1}{10}$

$P(\bar X = 11) = \dfrac{1}{10}$

$P(\bar X = 14) = \dfrac{1}{10}$