QUANTITATIVE & STATISTICAL ANALYSIS
UNIVERSITY OF LA VERNE COLLEGE OF BUSINESS AND PUBLIC MANAGEMENT BUS 500C QUANTITATIVE & STATISTICAL ANALYSIS COMPREHENSIVE FINAL EXAMINATION
1. The personnel director for a business organization has identified 10 individuals as qualified candidates for 3 managerial training positions her firms seeks to fill. Use the appropriate rule to give the number of different combinations of the 10 individuals who could be chosen for the 3 positions.
As discussed in class we would use the combination approach. The primary reason is that they are all identical (qualified) positions and thus the order would not matter.
Data: The variable is the total number of elements = n (3) and r (10) designates the number of groups and is expressed by the following formula from our textbook (Keller, 2012). The formula that produces the result of 120 combinations is. = 10! = 10x9x8x7x6x5x4x3x2x1 3628800 = 120 3(10-3)! (3x2x1)(7x6x5x4x3x2x1) = 6(5040)
2. The president, vice president, secretary, and treasurer are to be selected from a group of 10 candidates. Use the appropriate rule to give the number of ways the positions may be filled.
Based on class discussion and my studies, and the facts provided, the permutation rule would be used to determine the answer. Applying this formula there would be 5040 permutations.
Order would matter, because there is a order or value to the four positions and each of the candidates could be combined with the others in each position (e.g. A,B,C,D would each be paired with the others ABCD, DBCA, DBAC.) Therefore, if the first and last AB stayed the same, the others CD could change. The formula to prove this is:
10! = 10x9x8x7x6x5x4x3x2x1 = 3628800 = 5040 (10-4)! 6x5x4x3x2x1 720
3. Answer the following questions: Murph, the Union 76 gas station guy, has an average of 6 customers per hour stop for gasoline at his station.
A) What is the probability of exactly one customer
1. The personnel director for a business organization has identified 10 individuals as qualified candidates for 3 managerial training positions her firms seeks to fill. Use the appropriate rule to give the number of different combinations of the 10 individuals who could be chosen for the 3 positions.
As discussed in class we would use the combination approach. The primary reason is that they are all identical (qualified) positions and thus the order would not matter.
Data: The variable is the total number of elements = n (3) and r (10) designates the number of groups and is expressed by the following formula from our textbook (Keller, 2012). The formula that produces the result of 120 combinations is. = 10! = 10x9x8x7x6x5x4x3x2x1 3628800 = 120 3(10-3)! (3x2x1)(7x6x5x4x3x2x1) = 6(5040)
2. The president, vice president, secretary, and treasurer are to be selected from a group of 10 candidates. Use the appropriate rule to give the number of ways the positions may be filled.
Based on class discussion and my studies, and the facts provided, the permutation rule would be used to determine the answer. Applying this formula there would be 5040 permutations.
Order would matter, because there is a order or value to the four positions and each of the candidates could be combined with the others in each position (e.g. A,B,C,D would each be paired with the others ABCD, DBCA, DBAC.) Therefore, if the first and last AB stayed the same, the others CD could change. The formula to prove this is:
10! = 10x9x8x7x6x5x4x3x2x1 = 3628800 = 5040 (10-4)! 6x5x4x3x2x1 720
3. Answer the following questions: Murph, the Union 76 gas station guy, has an average of 6 customers per hour stop for gasoline at his station.
A) What is the probability of exactly one customer