{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Quiz4Sols

# Quiz4Sols - Solutions for Quiz 4 1 Suppose that 200 fair...

This preview shows pages 1–2. Sign up to view the full content.

Solutions for Quiz 4 1) Suppose that 200 fair dice are tossed. Estimate the chance that the sum of the 200 rolls is at least 715. a) Box Model: Draw from the following box and sum draws: [1, 2, 3, 4, 5, 6] Box Statistics: Box.avg = (1+2+3+4+5+6)/6 = 3.5 Box.sd = 1.707825 Sum of draws Statistics: 1) EV = 200*3.5 = 700 2) SE = sqrt(200)*1.707825 = 24.152295 Min = 200 Max = 1200 b) Normal Approximation: 1) Continuity Correction: Necessary since we have at least one pair of consecutive integers, endpoint is included, and # of draws is less than 10,000. 2) Convert 715-.5 = 714.5 to Standard Units, SU = (714.5 – EV)/SE = (714.5 – 700)/24.152295 = .600357 Area above this is, 50% – 0.5*Area(z=.600357) = 50% – 0.5*45.15% = 27.43 c) Normal Approximation Justification: 1) There are at least 25 draws 2) 700 – 2*SE > 200 and 700 + 2*SE < 1200 2) a) Box Model: Draw from the following box: [ From each pair of bets your net gain is either -\$2 (Lose, Lose), \$0 (Win, Lose), \$34 (Lose, Win), or \$36 (Win, Win). The chance of getting -\$2 is (20/38)*(37/38)= 740/1444 The chance of getting \$0 is (18/30)*(37/38) = 666/1444 The chance of getting \$34 is (20/38)*(1/38) = 20/1444 The chance of getting \$36 is (18/38)*(1/38) = 18/1444

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Quiz4Sols - Solutions for Quiz 4 1 Suppose that 200 fair...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online