Question

Problem: A populatio consists of the six numbers 4,9,11,7,8 and 3. Consider the sample of size 3 that can be drawn from this population?

What is N?

How many samples can be drawn in the population?

What is the probability of getting 8.67?

The probability of getting 6.33 is?

what is EP(x)?

Answer 1

$N=6 -\,\,size\,\,of\,\,population\\C_{6}^{3}=20\,\,samples\,\,can\,\,be\,\,drawn\\P\left( \bar{x}=8.67 \right) =P\left( \bar{x}=\frac{26}{3} \right) =\frac{1}{20}\\P\left( \bar{x}=6.33 \right) =P\left( \bar{x}=\frac{19}{3} \right) =\frac{2}{20}=\frac{1}{10}\\EP\left( \bar{x} \right) =\mu =\frac{3+4+7+8+9+11}{6}=7$