Sampling distribution involves the proportions of a data element in a given sample.
- <em>The proportion of Good TV set is 0.67</em>
- <em>The number of ways of selecting 5 from 6 TV sets is 6</em>
- <em>The number of ways of selecting 4 from 6 TV sets is 15</em>
<em />
Given

Sample Space = Good, Good, Defective, Defective, Good, Good
<u>(a) Proportion that are good</u>
From the sample space, we have:

So, the proportion (p) that are good are:



<u>(b) Ways to select 5 samples (without replacement)</u>
This is calculated using:

Where

So, we have:





Hence, there are 6 ways
<u>(c) All possible sample space of 4</u>
First, we calculate the number of ways to select 4.
This is calculated using:

Where

So, we have:





So, the table is as follows:
![\left[\begin{array}{ccc}TV&Good&Proportion\\1,2,3,4&2&0.5&2,3,4,5&2&0.5&3,4,5,6&2&0.5\\4,5,6,1&3&0.75&5,6,1,2&4&1&6,1,2,3&3&0.75\\1,2,3,5&3&0.75&3,5,6,2&3&0.75&1,3,4,5&2&0.5\\1,3,4,6&2&0.5&1,4,5,2&3&0.75&2,4,6,1&3&0.75\\2,4,6,3&2&0.5&2,4,6,5&3&0.75&3,5,6,1&3&0.75\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DTV%26Good%26Proportion%5C%5C1%2C2%2C3%2C4%262%260.5%262%2C3%2C4%2C5%262%260.5%263%2C4%2C5%2C6%262%260.5%5C%5C4%2C5%2C6%2C1%263%260.75%265%2C6%2C1%2C2%264%261%266%2C1%2C2%2C3%263%260.75%5C%5C1%2C2%2C3%2C5%263%260.75%263%2C5%2C6%2C2%263%260.75%261%2C3%2C4%2C5%262%260.5%5C%5C1%2C3%2C4%2C6%262%260.5%261%2C4%2C5%2C2%263%260.75%262%2C4%2C6%2C1%263%260.75%5C%5C2%2C4%2C6%2C3%262%260.5%262%2C4%2C6%2C5%263%260.75%263%2C5%2C6%2C1%263%260.75%5Cend%7Barray%7D%5Cright%5D)
The proportion column is calculated by dividing the number of Good TVs by the total selected (4) i.e.

<u>(d) The sampling distribution</u>
In (a), we have:
--- proportion of Good TV
The sampling error is calculated as follows:

So, we have:
![\left[\begin{array}{ccc}TV&Good&SE\\1,2,3,4&2&0.17&2,3,4,5&2&0.17&3,4,5,6&2&0.17\\4,5,6,1&3&0.08&5,6,1,2&4&0.33&6,1,2,3&3&0.08\\1,2,3,5&3&0.08&3,5,6,2&3&0.08&1,3,4,5&2&0.17\\1,3,4,6&2&0.17&1,4,5,2&3&0.08&2,4,6,1&3&0.08\\2,4,6,3&2&0.17&2,4,6,5&3&0.08&3,5,6,1&3&0.08\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DTV%26Good%26SE%5C%5C1%2C2%2C3%2C4%262%260.17%262%2C3%2C4%2C5%262%260.17%263%2C4%2C5%2C6%262%260.17%5C%5C4%2C5%2C6%2C1%263%260.08%265%2C6%2C1%2C2%264%260.33%266%2C1%2C2%2C3%263%260.08%5C%5C1%2C2%2C3%2C5%263%260.08%263%2C5%2C6%2C2%263%260.08%261%2C3%2C4%2C5%262%260.17%5C%5C1%2C3%2C4%2C6%262%260.17%261%2C4%2C5%2C2%263%260.08%262%2C4%2C6%2C1%263%260.08%5C%5C2%2C4%2C6%2C3%262%260.17%262%2C4%2C6%2C5%263%260.08%263%2C5%2C6%2C1%263%260.08%5Cend%7Barray%7D%5Cright%5D)
Read more about sampling distributions at:
brainly.com/question/10554762