A population consists of the five numbers 2,3,6,8 and 11. Consider all possible samples of 2 that can be drawn with replacement from this population (i.e. as soon as soon as number has been drawn and its value noted it is replaced and can be drawn again). Find

i) The mean of the population.

ii) The standard deviation of the population.

iii) The mean of the sampling distibution of means.

iv) The standard deviation of the sampling distribution of means.

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For i) I calculated the mean to be 6.0 however I found the standard deviation for part ii) to be 3.67 to which I am unsure of its reliability.

Can anyone please help with these please, I am keen to learn the method to solving these.

Regards