HOMEWORK #4 ANSWERS

Chapter 16

4. (a) 60 rolls. With more rolls, the percentage of aces will be closer to 16 2/3%. You want the percentage of aces to be far from 16 2/3%. Chance error in the percentages is working against you, choose the smaller number of rolls.

(b) 600 rolls. Now chance error in the percentages is working for you, choose the larger number of rolls.

(c) 600 rolls. Like (b).

(d) 60 rolls. As you roll more and more, there get to be more and more possibilities, no particular one can be very likely. Take a more extreme case: with 6000 rolls, you can get 1000 aces, or 1001, or 1002,…. There are lots of possibilities, each one individually has a small chance.

10 (a) 30/200 = 0.15.

-0.1.

Average = sum/200.

(d) The same: 5/200 = 0.025, so the options describe the same event in different language.

Chapter 17

4. The number of aces in 180 rolls of a die is like the sum of 180 draws from a box with 1 ticket marked "1" and 5 tickets marked "0". The number of aces will be around 30, give or take 5 or so. There is about a 99.7% chance that the number of aces will be in the range 15 to 45. About 99.7% of the people should get a number in that range.

8. (a) Option (ii) is right. The sum is equally likely to go up or down 1 on each draw, just like the difference. Option (i) is out, you can't add words; with option (iii), the sum can't go up; with option (iv), the sum can't go down; with option(v), the sum has a chance to stand still, but the difference has to go up or down.

(b) Expected value = 0. SE = the squareroot of 100 = 10.

Chapter 18

5. (i) is the probability histogram for the sum, it's like the normal curve.

(ii) is the probability histogram for the product, it's like figure 10, p. 323.

(iii) is the histogram for the numbers drawn, it's like a histogram for the numbers in the box.

11. The sum of the draws is 270, with EV = 250 and SE = 15; the chance error is 20, which is 1.33 SEs. The number of 1's is 17, with EV = 25 and SE . 4.33; the chance error is -8, which is about -1.8 SEs. The number of 2's is 54, with EV = 50 and SE = 5; the chance error is 4, which is 0.8 SEs.

(a) number of 2's

(b) sum of the draws

Chapter 19

2. No, because of response bias. The subjects could try to give the interviewers the pleasing answer, rather than the true answer. (In this study, many respondents said they were using the product when they really weren't.)

10. Look at figure 3, chapter 18. The likeliest number of heads is 50: pick that first. Your next two picks should be 49 and 51. Then 48 and 52. And so forth. You should pick 45 through 55. And your chance of winning is about 73%--example 1(b) on p. 317.

DISC (Lab manual)

7. 58.5 years