BUS 304 Homework Assignment #3, Due date: July 21, 2008 Submitted by: (sign) Submission date: (sign) Page 137 – 138 Problem #1: Exercise 4.2 Frequency Table: Model Color Blue Brown White Total XB-50 302 105 200 607 YZ-99 40 205 130 375 Total 342 310 330 982 a) P (Brown) = 310/982 =0.3157 b) P(YZ-99) = 375/982 = 0.3819 c) P(YZ-99 & Brown) = 205/982 = 0.2088 d) P(YZ-99 & White) = 130/982 = 0.1324 ≠ 0 Î “Choosing YZ-99” and “Choosing White” are not mutually exclusive events. Problem #2: Exercise 4.5 P (raining) = 25/200 =0.125 P (not raining) = 1 – 0.125 = 0.875 Problem #3: Exercise 4.8 Questions (a) and (c) a) P (help-wanted) = 204 / (204+520+306) = 0.1980 b) Skipped c) They are mutually exclusive because there is only one ad can be chosen. If it is a help-wanted ad, it cannot be an ad for other types of products or services. Problem #4: Exercise 4.10 (Note the manager assigned probability based on his experience) a) The manager is very likely to use subjective probability assessment. It doesn’t see that the manager has any past data and frequency table to use relative frequency method. b) It doesn’t make sense to use classical probability assessment. There is no clearly defined elementary event, and there is no way showing that the elementary events are equally likely to happen. Problem #5: Exercise 4.11 Questions (a) and (b) a) P(female) = 130/(130+150) = 0.4643 b) Relative Frequency.Page 156 Problem #6 Exercise 4.16 Model A B C Total D 100 150 50 300 E 600 150 150 900 F 300 300 300 900 Total 1000 600 500 2100 a) P (A) = 1000/2100 = 0.4762 b) P (A & B) = 0 c) P (B & F) = 300/2100 = 0.1429 d) P (E | A) = 600/1000 = 0.6 e) P (A or F) = P(A) + P(F) – P(A&F) = 1000/2100 + 900/2100 – 300/2100 = 0.7619 Problem #7 Exercise 4.17 a) P (Dry) = P (Clear&Dry) + P(Cloudy&Dry) =0.2+0.3=0.5 b) P(Rainy Or Cloudy&Dry) = P(Rainy) + P(Cloudy&Dry) = 0.4 + 0.3=0.7 c) P(Cloudy | Dry) = P(Cloudy&Dry)/P(Dry) =0.3/(0.2+0.3) = 0.6 Page 167 - 168 Problem #8 Exercise 4.40 x P(x) x*P(x) x-E(x) [x-E(x)]2 [x-E(x)]2*P(x) 10 0.05 0.5 -17.5 306.25 15.3125 15 0.2 3 -12.5 156.25 31.25 25 0.4 10 -2.5 6.25 2.5 40 0.35 14 12.5 156.25 54.6875 E(x) = 27.5 Var(x) =103.75 SD(x) =10.186Problem #9 Exercise 4.41 x P(x) x*P(x) x-E(x) [x-E(x)]2 [x-E(x)]2*P(x) 100 0.30 30 -38 1444 433.2 150 0.40 60 12 144 57.6 160 0.30 48 22 484 145.2 E(x) = 138 Var(x) =636 SD(x) =25.21904 Problem #10 Exercise 4.50 Questions a) - c). a) Convert to Pro Dist. Table: x P(x) 5 0.1 15 0.17 25 0.35 35 0.22 45 0.16 b) Expected Number x P(x) x*P(x) 5 0.1 0.5 15 0.17 2.55 25 0.35 8.75 35 0.22 7.7 45 0.16 7.2 E(x) = sum of this column = 26.7 c) Variance & Std. Dev. x P(x) x-E(x) [x-E(x)]2 [x-E(x)]2*P(x) 5 0.1 -21.7 470.89 47.089 15 0.17 -11.7 136.89 23.2713 25 0.35 -1.7 2.89 1.0115 35 0.22 8.3 68.89 15.1558 45 0.16 18.3 334.89 53.5824 Var = sum of above = 140.11 Sd (x) = sqrt(140.11) = 11.84 Page 170 Problem #11 Exercise 4.58