A company has offices in two different countries. Suppose that the average age (in years) of the employees at location A is 40.1
40.140, point, 1 with a standard deviation of 5.55.55, point, 5, and the average at location B is 36.736.736, point, 7 with a standard deviation of 6.36.36, point, 3.
Every month, the company takes separate random samples of 505050 employees from each location for a survey. Each time, they look at the difference in the mean age sampled from each location \left( \bar{x}_\text{A} - \bar{x}_\text{B} \right)(
x
ˉ
A
−
x
ˉ
B
)left parenthesis, x, with, \bar, on top, start subscript, start text, A, end text, end subscript, minus, x, with, \bar, on top, start subscript, start text, B, end text, end subscript, right parenthesis.
What do we know about the shape of the sampling distribution of \bar{x}_\text{A} - \bar{x}_\text{B}
x
ˉ
A
−
x
ˉ
B
x, with, \bar, on top, start subscript, start text, A, end text, end subscript, minus, x, with, \bar, on top, start subscript, start text, B, end text, end subscript, and why?
