Congratulations for being hired Director of Casino Services for the Adelphi Casi
ID: 3041860 • Letter: C
Question
Congratulations for being hired Director of Casino Services for the Adelphi Casino and Racetrack. On your second week of work, you received a state complaint filed by 132 patrons of the casino that the vendor WMS has sent faulty slot machines to your casino. The claim has indicated that some machines are not paying out at the claimed payout percentages. To that end, your staff has sampled over a five-hour period the number of times a bonus was initiated on the machines below:
Slot Machines - http://www.wms.com/Games/Video/IPlay/Pages/default.aspx
Jade Palace
The Princess Bride
Winning Bid 2
Jackpot Block Party
Airplane
1 p.m.
1
2
3
3
4
2 p.m.
1
6
2
3
4
3 p.m.
3
3
3
1
5
4 p.m.
2
7
7
5
8
5 p.m.
6
4
8
6
3
6 p.m.
7
3
4
4
6
The five machines initiate bonuses at a mean of 4.15/per hour and a SD of 2.06
The average money spent was $212 per hour and an SD of $294
The judge advanced five complainants who kept meticulous records. The judge has allowed you to use the sum for each complainant for the bonuses (i.e. Add up each bonus per complainant and find the mean. Then convert the mean into a z-score and then find the area. You also find the z-score for the money spent per complainant.)
Money
Spent
Jade Palace
The Princess Bride
Winning Bid 2
Jackpot Block Party
Airplane
Complainant 1
$300
7
6
4
2
11
Complainant 2
$550
8
3
6
7
2
Complainant 3
$75
3
6
22
6
4
Complainant 4
$688
9
15
0
8
4
Complainant 5
$290
4
4
11
8
5
% Above in Money Spent
% Over in Bonuses Per Hour
Complainant #1
Complainant #2
Complainant #3
Complainant #4
Complainant #5
To make the decision below, the complainant must be above 65% of their class action suit group in Money Spent and over 85% in Bonuses per hour. If they exceed both metrics, then the complainant lost their case.
1) Did complainant #1 win the case? YES NO
2) Did complainant #2 win the case? YES NO
3) Did complainant #3 win the case? YES NO
4) Did complainant #4 win the case? YES NO
5) Did complainant #5 win the case? YES NO
6) You won your lawsuit if the majority of the complainants lost. Did you win your case?
(provide evidence at the end of the document.)
Slot Machines - http://www.wms.com/Games/Video/IPlay/Pages/default.aspx
Jade Palace
The Princess Bride
Winning Bid 2
Jackpot Block Party
Airplane
1 p.m.
1
2
3
3
4
2 p.m.
1
6
2
3
4
3 p.m.
3
3
3
1
5
4 p.m.
2
7
7
5
8
5 p.m.
6
4
8
6
3
6 p.m.
7
3
4
4
6
Explanation / Answer
Find the average of 5 bonus hrs spent (jade, princess, winning, jackpot, airplane)
Find the z-score by the formula (x-mu)/ sigma. Mu (average) is 4.15 and sigma (std devn) is 2.06
find the % in bonus hours using the formula norm.s.dist(z-score, True)
find the z-score for money spent by the formula (x-mu)/ sigma. Mu (average) is 212 and sigma (std devn) is 294
find the % money spent using the formula norm.s.dist(z-score, True)
Taking the benchmarks of 65% for % money spent and 85% for %bonuses per hour, only complainant 4 won the case.
1) Did complainant #1 win the case?
NO
2) Did complainant #2 win the case?
NO
3) Did complainant #3 win the case?
NO
4) Did complainant #4 win the case?
YES
5) Did complainant #5 win the case?
NO
6) You won your lawsuit if the majority of the complainants lost. Did you win your case?
Yes. We won the case.
Moneyspent Jade
Palace The Princess
Bride Winning
Bid 2 Jackpot
Block Party Airplane Mean hrs z-score % in bonus/ hr Mean money spent Complainant 1 300 7 6 4 2 11 6 0.898058 81.5% 0.29932 62% Complainant 2 550 8 3 6 7 2 5.2 0.509709 69.5% 1.14966 87% Complainant 3 75 3 6 22 6 4 8.2 1.966019 97.5% -0.46599 32% Complainant 4 688 9 15 0 8 4 7.2 1.480583 93.1% 1.619048 95% Complainant 5 290 4 4 11 8 5 6.4 1.092233 86.3% 0.265306 60%
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