6. Possibility (i) is better. Reason: 10/15 = 20/30 = 2/3. Option (i) is like tossing a coin 15 times, and asking for 2/3 or more heads. Option (ii) ups the number of tosses to 30. With the bigger number of tosses, you are less likely to get 2/3 or more heads. This is like exercise 4(a).

 7. The score is like the sum of 25 draws from the box

 10. (a) 30/200 = 0.15.

2. -0.1.
3. Average = sum/200.

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

language.

6.

12 chance error in the sum of the draws

45 observed value for the number of 1's

187 observed value for the sum of the draws

25 expected value for the number of 3's

50 expected value for the number of 1's

175 expected value for the sum of the draws

5 standard error for the number of 1's

32 observed value for the number of 3's

 7. (a) 321/100 = 3.21.

(b) 3.78 x 100 = 378.

(c) The average of the draws will be between 3 and 4 when the sum is between 300 and 400. The expected value for the sum is 350, and the SE is x 1.7 = 17,

so the chance is about 99.7%.

 Chapter 18

  (b) The number of 3's is like the sum of 400 draws from the box | 0 1 0 0 |. The

expected number is 100 and the SE is 8.66. The chance is about 12%.

 Comment. The continuity correction could be used for part (b) if more accuracy

were needed.

 14. This is like drawing at random with replacement from a box with 4 tickets marked

"1" and 6 marked "0", and asking for the chance that the sum of the draws will be

425 or more. The normal approximation will be fine. (The average and SD of the

original numbers in the box are irrelevant.)

 Chapter 19

 5. This estimate is likely to be too high. With smaller households, the interviewer is less likely to find someone at home. So the survey procedure is, on average, replacing smaller households by larger ones.

 6. No. Different sorts of students are more likely or less likely to walk through different parts of the campus at different times, and the chances are diffficult or impossible to figure (p.341).

 11. (a) 10 through 20.

(b) 40 through 50.

(c) To get the center of the range, take 50 from the sum; and then go 5 either way.

(d) 73%, as in the previous exercise.