Question

Suppose that you are a student aide in the library and agree to be paid according to the "random pay" system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is 80$.Ifitcomesuptails,yourpayfortheweekis40$. You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings ${\mathrm{x}}^{-}\overline{x}$. The shape of the sampling distribution of will be

a. Normal.

b. approximately Normal.

c. right-skewed.

d. left-skewed.

e. symmetric but not Normal.

Short answer

(e). The sample distribution will be symmetric but not normal in shape.

Step-by-step solution

Given Information

The following options are

a. Normal.

b. approximately Normal.

c. right-skewed.

d. left-skewed.

e. symmetric but not Normal.

Explanation for correct option

A basic arbitrary sample has a duration of two weeks, with an average duration of two weeks. Because it can get $40\$$ during the first week, it is twice as likely to get 60$, then 40$, and finally $80\$$.

As a result, the distribution would be symmetric about $\$60$, but otherwise normal.

As a result, the best solution is (e)

Explanation for incorrect option

a. The shape of the sampling distribution of will not be Normal

b. The shape of the sampling distribution of will not be approximately Normal

c. The shape of the sampling distribution of will not be right-skewed.

d. The shape of the sampling distribution of will not be left-skewed .