Project #75752 - ANALYTICAL METHODS HELP NEED

Problem 1

 

An urn contains 40 balls, of which 18 are red and the other 22 blue. Suppose you take out 12 balls from this urn, without replacement. What is the probability that exactly 5 are red and 7 are blue among the 12 balls you choose?

 

Problem 2

 

Ten chairs in a row are to be occupied by seven students and Professors Alpha, Beta, and Gamma. These three professors arrive before the seven students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professors Alpha, Beta, and Gamma choose their chairs?

 

Problem 3

 

Eight people get into an elevator at the ground floor of a hotel which has 11 upper floors. Assuming each person gets off at a randomly chosen floor, what is the probability that no two people get off at the same floor?

 

Problem 4

 

A random variable X is binomially distributed with mean 6 and variance 4.2. What is P(X ≤ 5)?

 

Problem 5

 

Each student is likely to be absent from a class 15% of the time. A class is cancelled if the number of attendants is not more than 11 out of the total registered 100. What is the expected numbers present in a class and what is the probability that a class will be canceled?

 

Problem 6

 

Answer the following problem from Bertsimas, Dimitris, and Robert Freund. Data, Models, and Decisions: The Fundamentals of Management Science. Charlestown, MA: Dynamic Ideas, 2004. ISBN: 9780975914601.

 

Chapter 4, p185

Housing Prices in Lexington, Massachusetts

 

 

 

 

 

Table 4.6: VALMAX Sales

House

Asking Price

Selling Price

Difference

Number

($)

($)

($)

1

290,000

275,000

15,000

2

315,000

314,000

1,000

3

299,000

310,000

-11,000

4

615,000

610,000

5,000

5

345,000

345,000

0

6

230,000

221,000

9,000

7

420,000

418,000

2,000

8

399,000

382,000

17,000

9

549,000

555,000

-6,000

10

299,000

292,000

7,000

11

430,000

431,000

-1,000

12

330,000

303,000

27,000

13

395,000

381,000

14,000

14

675,000

661,000

14,000

15

460,000

443,000

17,000

16

437,000

449,000

-12,000

17

680,000

668,000

12,000

18

380,000

385,000

-5,000

19

325,000

310,000

15,000

20

435,000

435,000

0

21

304,000

300,000

4,000

22

552,000

560,000

-8,000

23

403,000

389,000

14,000

24

419,000

425,000

-6,000

25

227,000

217,000

10,000

26

340,000

342,000

-2,000

27

619,000

615,000

4,000

28

312,000

308,000

4,000

29

320,000

319,000

1,000

30

299,000

270,000

29,000

31

289,000

280,000

9,000

32

316,000

319,000

-3,000

33

328,000

320,000

8,000

34

610,000

615,000

-5,000

35

350,000

353,000

-3,000

 

 


 

Table 4.7: Others Sales

House

Asking Price

Selling Price

Difference

Number

($)

($)

($)

1

295,000

280,000

15,000

2

425,000

411,000

14,000

3

299,000

285,000

14,000

4

299,000

299,000

0

5

475,000

471,000

4,000

6

350,000

348,000

2,000

7

429,000

418,000

11,000

8

399,000

401,000

-2,000

9

489,000

476,000

13,000

10

299,000

270,000

29,000

11

539,000

531,000

8,000

12

225,000

214,000

11,000

13

749,000

735,000

14,000

14

689,000

664,000

25,000

15

469,000

476,000

-7,000

16

299,000

270,000

29,000

17

539,000

531,000

8,000

18

199,000

205,000

-6,000

19

349,000

335,000

14,000

20

689,000

687,000

2,000

21

485,000

479,000

6,000

22

299,000

285,000

14,000

23

305,000

275,000

30,000

24

479,000

469,000

10,000

25

699,000

677,000

22,000

26

339,000

325,000

14,000

27

195,000

209,000

-14,000

28

539,000

535,000

4,000

29

279,000

268,000

11,000

30

459,000

469,000

-10,000

31

679,000

659,000

20,000

32

729,000

725,000

4,000

33

215,000

214,000

1,000

34

539,000

525,000

14,000

35

289,000

270,000

19,000

36

479,000

469,000

10,000

37

389,000

390,000

-1,000

38

419,000

410,000

9,000

39

339,000

339,000

0

40

469,000

462,000

7,000

41

299,000

280,000

19,000

42

289,000

280,000

9,000

43

419,000

403,000

16,000

44

289,000

275,000

14,000

Subject Mathematics
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