Pranav and Kristin are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Pranav sold 11 rolls of plain
wrapping paper and 13 rolls of holiday wrapping paper for a total of $122. Kristin sold 5 rolls of
plain wrapping paper and 14 rolls of holiday wrapping paper for a total of $104. What is the cost
each of one roll of plain wrapping paper and one roll of holiday wrapping paper?

Five hundred draws are made at random from the box:

True or false?

(a) The expected value for the percentage of 1’s among the draws is exactly 25%.

(b) The expected value for the percentage of 1’s among the draws is around 25%, give or take 2% or so.

(c) The percentage of 1’s among the draws will be around 25%, give or take 2% or so.

(d) The percentage of 1’s among the draws will be exactly 25%.

(e) The percentage of 1’s in the box is exactly 25%.

(f) The percentage of 1’s in the box is around 25%, give or take 2% or so.

(a) True

(b) False

(c) True

(d) False

(e) True

(f) False

Step-by-step explanation:

From (a);

We can infer that the  expected value for the percentage of 1’s among the draws is exactly 25% is true.

Because ; average of the box =

average of the box =

average of the box = 0.25

Thus; the expected value is said to be ; 25%

(b) The expected value for the percentage of 1’s among the draws is around 25%, give or take 2% or so.

Well!, this is false.

Because  the expected value for the percentage of 1's among the draws is 25% ,as a result of that there won't be any give and take due to the fact that the expected value involves no probability error.

(c) The percentage of 1’s among the draws will be around 25%, give or take 2% or so.

This is true.

If we determine the standard deviation of the box ; we have :

The standard error of the sum can now be calculated as :

= 0.433 ×√500

= 9.682

The standard error of the percentage of 1's is:

= 1.9364%

≅ 2%

(d) The percentage of 1’s among the draws will be exactly 25%

It is clear and obvious that this is false because if we look at what we have in (c) from above ; we will realize that the percentage of 1's among the draws will be around 25% and not exactly 25%

(e) The percentage of 1’s in the box is exactly 25%.

Yes; this is true. The  percentage of 1’s in the box is exactly 25%.

(f) The percentage of 1’s in the box is around 25%, give or take 2% or so.

No; this is false. The percentage of  1’s in the box is exactly 25% and not around  25%, give or take 2% or so.