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Quantitative Methods Chap 2 Problems

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Submitted By djsiv
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Quantitative Methods for Business

Page 51-57. Problems: 2 (a,b,c), 5 (a,b), 9,10,17 (a,b,c,d,e),21 (a,b,c),23 (a,b)
Case Problem: pg 61, College Softball Recruiting
2.
a. define experiment: choose a person at random, and have them taste the different blends of coffee and state a preference. b. ¼ per blend, classical method c. P1(.20), P2(.30), P3(.35), P4(.15)= Σ Pᵢ =1.00
5.
a. Not valid, Σ Pᵢ must equal 1 and they do not. b. Increase the probability values to equal 1.
9. Σ ᵢ=250 Eyes | Rash | Both | 90 | 135 | 45 | P(A) | P(B) | P(A∪B) | P(A)=.36 P(B)=.54 P(A∪B)=.18
P(A∩B)= P(A) + P(B) – P(A∪B) = .36+.54 -.18= .72

10. P(defective and minor)= 4/25 P(defective and major)= 2/25 P(defective)= 6/25 P(Major│defective) = P(defective ∪ major)/ P(defective)= (2/25)/(6/25)= 1/3 or .33333
17. Σ ᵢ=989 (M) Male=759 (F) Female=230 | 1 game P(A) | > 1 game P(B) | Ttl P(A∪B) | Male | 582 (.59) | 177 (.18) | 759 (.77) | Female | 211(.21) | 19 (.02) | 230 (.23) | Ttl | 793 (.80) | 196 (.20) | 989 (1.0) | a .20 randomly selected fan attended multiple games. 196/989 b .90 random selected fan attend multiple games be male. 177/196 c .18 random selected fan being male and attended multiple games. 177/989 d .23 177/759
e. .79 random fan is male or has attended multiple games .77 + .20 - .18= .79

21. Prior Conditional Joint Posterior Aᵢ | P(Aᵢ) | P(B│Aᵢ) | P(Aᵢ∩B) | P(Aᵢ│B) | A1 Yes | .50 | .75 | .375 P(Aᵢ∩B) / | .65 | A2 No | .50 | .40 | .20 P(B) | .35 | | | P(B)= | .575 | |
a. .50 prior prob of yes
b. .75 conditional prob of yes
c. .65 posterior prob of yes

23. margins as above A1 high Q | .50 | .20 | .10 | .44 | A2 med Q | .20 | .20 | .04 | .17 | A3 no oil | .30 | .30 | .09 | .39 | | .23

a. .70 prob of finding oil
b. .61 prob of finding oil posterior prob

College Softball recruiting BA-Jr BA-Sr Fran | .35 | .38 | Millie | .34 | .37 |

a. Based on BA I would chose Fran
b. Based on combined BA for both yrs I would chose Millie @ .36 vs. Fran @ .35
c. Millie for consistency in relation to frequency of at bats, better long run pick
d. “While both ladies are exemplary examples of what we are looking for in student athletes, we are only allowed to chose one. Upon segregated analysis of both girls Junior and Senior years, it appeared that Fran had a slight advantage over Millie in her batting average per season. Once an aggregate assessment or “career to date” average was determined, It became clear that Millie had a stronger overall average in relation to the frequency of at-bats. This leads us to believe that Millie is the best candidate.
R/DJSIII

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