Answer to Question #315860 in Statistics and Probability for Fionamae

Question

Activity 2. (List and Construct)

A group of students got the following scores in an achievement test:

9,12,15,18, 21, and 24. Consider samples of size 3 that can be drawn from this

population

a. Determine and list all possible samples and the corresponding sample

means.

Random Samples

Sample Means

Probability

b. Construct a sampling distribution of the resulting sample means

Frequency

Sample Means

Answer 1

$a:\\\left( 9,12,15 \right) ,\bar{x}=12\\\left( 9,12,18 \right) ,\bar{x}=13\\\left( 9,12,21 \right) ,\bar{x}=14\\\left( 9,12,24 \right) ,\bar{x}=15\\\left( 9,15,18 \right) ,\bar{x}=14\\\left( 9,15,21 \right) ,\bar{x}=15\\\left( 9,15,24 \right) ,\bar{x}=16\\\left( 9,18,21 \right) ,\bar{x}=16\\\left( 9,18,24 \right) ,\bar{x}=17\\\left( 9,21,24 \right) ,\bar{x}=18\\\left( 12,15,18 \right) ,\bar{x}=15\\\left( 12,15,21 \right) ,\bar{x}=16\\\left( 12,15,24 \right) ,\bar{x}=17\\\left( 12,18,21 \right) ,\bar{x}=17\\\left( 12,18,24 \right) ,\bar{x}=18\\\left( 12,21,24 \right) ,\bar{x}=19\\\left( 15,18,21 \right) ,\bar{x}=18\\\left( 15,18,24 \right) ,\bar{x}=19\\\left( 15,21,24 \right) ,\bar{x}=20\\\left( 18,21,24 \right) ,\bar{x}=21\\b:\\P\left( \bar{x}=12 \right) =0.05\\P\left( \bar{x}=13 \right) =0.05\\P\left( \bar{x}=14 \right) =0.1\\P\left( \bar{x}=15 \right) =0.15\\P\left( \bar{x}=16 \right) =0.15\\P\left( \bar{x}=17 \right) =0.15\\P\left( \bar{x}=18 \right) =0.15\\P\left( \bar{x}=19 \right) =0.1\\P\left( \bar{x}=20 \right) =0.05\\P\left( \bar{x}=21 \right) =0.05$