:2. Solution. We need the EV and SE of the average of 100 draws from the box. To find these, we first get the EV and SE of the sum of 100 draws. The box average is 100, so the EV of the sum of the draws is 100 x 100 = 10,000. The box SD is 20, so the SE of the sum of the draws is 10 x 20 = 200. To find the corresponding quantities for the average of the draws, we divide each by the number of draws. The EV of the average of the draws is 10,000/100 = 100. The SE of the average of the draws is 200/100 = 2. Since
(98 - 100)/2 = -2/2 = -1 and (102 - 100)/2 = 2/2 = 1 ,
The chance that the average of the 100 tickets in the sample is between 98 and 102 is approximately equal to the area under the normal curve between -1 and 1, which is 68%.