# Assume a population of 2, 6, and 7. 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 2,6 2,7 6.2 6,6 6,7 7.2 7,6 7,7 a. Find the value of the population standard deviation o. = 2.160 Round to three decimal places s needed.) 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. Probability Type integers or fractions.)

Question

Assume a population of

2
​,
6
​,

and

7
.

Assume that samples of size

nequals
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

​,6

2

​,7

 6

​,2

 6

​,6

6

​,7

7

​,2

7

​,6

7

​,7

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

sigma

equals2.160

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

0.5
0.5
0
nothing
 ▼   0.707 1 2.5 nothing ▼   8 2.828 5 nothing ▼   6.4 3.536 12.5 nothing
​(Type integers or​ fractions.)

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