Assume a population of 2​,4​, and 9. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below.   2​,2 2​,4 2​,9 4​,2 4​,4 4​,9 9​,2 9​,4 9​, a. Find the value of the population standard deviation σ. σ=2.94392 Part B: Find the standard deviation of each of the nine​ samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations.   s Probability     ▼1.8 0 1       ▼1.414 2 2.5       ▼   6.4 3.536 12.5     ▼   4.95 24.5 7   ​(Type integers or​ fractions.) ​(Round to three decimal places as​ needed.)

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Assume a population of 2​,4​, and 9. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below.

 

2​,2

2​,4

2​,9

4​,2

4​,4

4​,9

9​,2

9​,4

9​,

a. Find the value of the population standard deviation σ.

σ=2.94392

Part B: Find the standard deviation of each of the nine​ samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations.

 

s

Probability

 

 

▼1.8

0

1

 

 

 

▼1.414

2

2.5

 

 

 

 

6.4

3.536

12.5

 

 

 

4.95

24.5

7

 

​(Type integers or​ fractions.)

​(Round to three decimal places as​ needed.)

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