# 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 Due By (Pacific Time) 07/18/2015 12:00 am
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