In earlier class units, we saw that a dataset that included the mean values derived from sampling from a dataset with an unknown distribution could be treated as a new random variable, and that this new variable had several important properties. explain how collecting mean values (x-bar) from samples drawn from a dataset, regardless of the statistical distribution of the dataset, results in a distribution of those values that is centered on the mean value of the original dataset and is approximately normally distributed depending upon the sample size used. include the name the theorem that describes this phenomenon, and discuss what it means to treat the x-bar data points derived from sampling as a new random variable. why is this important in engineering?

8

step-by-step explanation:

just put √(2) * √(32) into a calculator. that will make the answer be 8.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

the answer is 40.

proof: