Answers to the Review questions from Homework 3
Review Exercise Answers (Chapter 17)
1 (a) 100, 1000 (b) The average of the box is 7 and the SD of the box is 3. So the expected value for the sum of 100 draws is 700 and the Standard Error is SQRT(100) x 3 = 30. The chance is about 90% that the sum will be between 650 and 750.For (a), if by some chance you drew the "1" 100 times, your sum could be as low as 100. If by some chance you drew the 10 100 times, you can get a sum as high as 1000.
For (b), to figure out the chance of getting a sum between 650 and 750, use the normal approximation. 650-700/30 = -50/30 = -1.67 and (750 - 700)/30 = 50/30= 1.67 these are Z scores. Round them to about 1.70 gives about 90% between the two.
7. (a) 321/100 = 3.21
(b) 3.78*100 = 378
(c) The average of the box is 3.5, for 100 draws, the expected
sum is 350 and the expected sum over 100 draws for averages of 3
and 4 is 300 and 400 respectively. The SD of the box is 1.7 and
the SE of the box for 100 draws is SQRT(100) x 1.7 = 17.
So the chance that the average will be between 3 and 4 is
400 - 350 / 17 = 2.94 and 300 - 350 / 17 = -2.94 is about 99.7%
In other words, it would be difficult to get less than 300 or more
than 400 from this particular box.