HOMEWORK #3 ANSWERS

Chapter 6

 5. (a) No. Persons 2 and 10 copied from each other: they got exactly the same answers, with the decimal point in the wrong place. The other students seem to have worked independently.

(b) First, nobody got the same answer both times. Second, there is a lot of person-to-person variation.

Chapter 6 Special Review Exercises

 3. We can get the SD by looking at the first two scores, in original units and in standard units: 79 - 64 = 15 points, while 1.8 - 0.8 = 1 .0. So, 1 .0 SD = 15 points, and the SD is 15 points. Next, we get the average from the fact that 64 is 0.8 in standard units: 0.8 SD = 12 points, so the average must be 64 - 12 = 52. Finally, we complete the table:

  52 72 31

  0 1.33 -1.4

 

7. The average is 630; again, the SD is more than 125.

 9. Average = 10 - 6.4 = 3.6 and SD = 2.0

Reason: number wrong = 10 - number right

 11. By symmetry, the average is half way between the 25th and 75th percentiles, and is 64.0 inches. The 75th percentile is about 0.67 SDs above average, so, the SD is (65.8 - 64.0)/.67 » 2.7 inches. The 90th percentile is about 1.28 SDs above average, that is, 64.0 + 1.28 x 2.7 » 67.5 inches.

 Chapter 13

 3. Option (ii) is better, because there are a lot more ways to win:

clubs diamonds hearts spades

hearts diamonds clubs spades

etc.

 4. 4/52 x 3/51 x 2/50 x 1/49 x 4/48 » 1/3,000,000

 9. (a) (1/6)10 = 1/60,466,176

(b) 1 - 1/60,466,176 » 1

(c) (5/6)10 » 0.16, or 16%

  Comment. Not getting 10 sixes is easier than getting 10 non-sixes.

 11. Option (ii) is better. You have the same 50-50 chance of winning $1, but you can't lose.

 12. 3/100 x 2/99 x 1/98 » 6/1,000,000