The ages​ (years) of three government officials when they died in office were 56​, 46​, and 60. complete parts​ (a) through​ (d).a. assuming that 2 of the ages are randomly selected with​ replacement, list the different possible samples.

Respuesta :

There are 9 possible samples for selection of two with replacement. 

They are: (56, 56) (56, 46) (56, 60) (46, 46) (46, 56) (46, 60) (60, 60) (60, 46) (60, 56)

Remember that when making solution sets with replacement you have the possibility of choosing the same number (or data point) twice. So in this case, you will have the number of possible answers squared for total possible answers. 

A sample is simply a part of an overall population.

The possible samples are: (56, 56) (56, 46) (56, 60) (46, 46) (46, 56) (46, 60) (60, 60) (60, 46) (60, 56)

The given parameters are:

[tex]\mathbf{n = 3}[/tex] --- the number of ages

[tex]\mathbf{r = 2}[/tex] -- the number of selection.

The total number of possible sample (s) is:

[tex]\mathbf{s = n^r}[/tex]

So, we have:

[tex]\mathbf{s = 3^2}[/tex]

[tex]\mathbf{s = 9}[/tex]

The above equation means that:

The total samples for selection of two with replacement is 9

The samples are generated by selecting two of 54, 46 and 60 at a time.

So, we have:  

[tex]\mathbf{Samples = \{(56, 56) (56, 46) (56, 60) (46, 46) (46, 56) (46, 60) (60, 60) (60, 46) (60, 56)\}}[/tex]

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