Q.10 - The Practice of Statistics for AP

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 $\backslash (80$. If it comes up tails, your pay for the week is $\backslash )40$. You work for the library for $100$ weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x. The shape of the sampling distribution of x will be 

(a) Normal. 

(b) approximately Normal 

(c) right-skewed 

(d) left-skewed.  

(e) symmetric but not Normal.

Step-by-Step Solution

Answer

The Correct answer is (e)

Step 1 Given Information

Payment for the week if the coin comes up heads $=\$80$

Payment for the week if the coin comes up tails $=\$40$

Number of weeks of work$=100$

Number of weeks for SRS = 2

Step 2 Explanation

Given the number of the week for SRS is $2 .$

This means the average amount could be $\$40$ for two weeks,$\$80$ for two weeks, or $\$60$ ( $\$40$ for one week and $\$80$ for the other week).

It is seen that getting $\$60$is twice likely because on the first week $\$40$ can be obtained and $\$80$ on the second week or vice versa.

Thus, the distribution will be symmetric  $\$60$ and it will also be normal.

Hence, the correct answer is (e).