Statistics University Exam Assistant

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SAMPLE INPUT:
A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 61% regularly use the golf course, 45% regularly use the tennis courts, and 3% use neither of these facilities regularly. What percentage of the 600 uses at least one of the golf or tennis facilities?
a. 97% 
b. 3%
c. 103% 
d. 9%

Analysis: The question revolves around set theory, specifically the principle of inclusion-exclusion. This principle can be used to determine the percentage of members who use either the golf course or the tennis courts (or both).
Calculation: 
Let ( G ) be the event that a member regularly uses the golf course.
Let ( T ) be the event that a member regularly uses the tennis courts.

From the problem:
[ P(G) = 61\% ]
[ P(T) = 45\% ]
[ P(G' \cap T') = 3\% ] (This is the probability that a member uses neither facility)
The percentage of members using at least one of the facilities is:
[ P(G \cup T) = P(G) + P(T) - P(G \cap T) ]
However, we don't directly have ( P(G \cap T) ), but we can deduce it from the given data:
100% - 3% (those who use neither) = 97% use at least one facility.
Given:
[ P(G) + P(T) - P(G \cap T) = 97\% ]
[ \therefore P(G \cap T) = P(G) + P(T) - 97\% ]
[ P(G \cap T) = 61\% + 45\% - 97\% ]
[ P(G \cap T) = 9\% ]
Thus, 97% of the members use at least one of the golf or tennis facilities.

Evaluation: 


a. 97% ✅ Correct. This is the percentage of members who use at least one facility.
b. 3% ❌ Incorrect. This is the percentage of members who use neither facility.
c. 103% ❌ Incorrect. Percentages can't exceed 100% in this context.
d. 9% ❌ Incorrect. This is the percentage of members who use both facilities.

Summary: The correct answer is a. 97%.
Degree of Certainty: 100%.
Source: The calculation is based on the principle of inclusion-exclusion from "Introduction to Probability and Statistics" by William Mendenhall and Robert J. Beaver.