Performance Summary

The 1^st Hourly

Math 1107

Fall 2002

Scores Summary

n	min	p25	mean	median	p75	max	p10	p20	p30	p40	p50	p60	p70	p80	p90
94	8	70	79.8085	84	92	100	61	68	74	79	84	86	90	95	99

The maximum score possible was 100 points; distributed over four cases, 25 points per case.

There were 94 scores.

The minimum scores were 8 and 10, respectively.

Approximately 75% of scores exceeded 70.

The mean score was approximately 80.

Approximately 25% of scores exceeded 92.

The maximum score was 100, and there were 9 of them.

Approximately 90% of scores exceeded 61.

Approximately 80% of scores exceeded 68.

Approximately 70% of scores exceeded 74.

Approximately 60% of scores exceeded 79.

Approximately 50% of scores exceeded 84.

Approximately 40% of scores exceeded 86.

Approximately 30% of scores exceeded 90.

Approximately 20% of scores exceeded 95.

Approximately 10% of scores exceeded 99.

Score Range	Frequency	Percent
<60%	9	9.57
60%-69%	13	13.83
70%-79%	16	17.02
80%-89%	25	26.60
90%-99%	22	23.40
100%	9	9.57

Score Range	Frequency	Percent
<60%	9	9.57
60%-69%	13	13.83
70%-79%	16	17.02
80%-89%	25	26.60
90%-100%	31	32.98

Case Commentary

Case 1

Part 1a) required the use of the multiplication rule (MR). The idea was to calculate all 9 probabilities, with full

detail on at least 4 pairs.

Parts 1b) and 1c) required the calculation of probabilities for each distinct value of the random variables LowTie

and Sum, using the additive rule (AR).

Case 2

The idea was to follow the same procedure as in Case Study 1.13. That is, remove the marbles as indicated

in the given event, and to then compute the probability directly by inspecting the resulting bowl. I did my best

to assess partial credit.

Case 3

Part 3a) required the use of the additive rule.

Part 3b) required the use of the complementary rule.

Case 4

This case required specific calculations and discussions. See the key for detail.