outine, 21% get a medium effort routine, and the rest get a low effort routine. After the first six months as members, the gym surveys the members’ adherence to the recommended routine. The gym classifies a member’s performance as optimal if they follow the recommended routine for the six months, or as inferior otherwise. According to the historical results of the survey, 84% of the members with a low effort routine, 22% of the members wit
A gym wishes to evaluate the effectiveness of its programs. When a new member joins the gym, they meet with a trainer who designs a recommended routine based on the member’s current fitness and their goals. The recommended routines can be classified into high, medium, or low effort. Historically, 68% of the new members get a high effort routine, 21% get a medium effort routine, and the rest get a low effort routine.
After the first six months as members, the gym surveys the members’ adherence to the recommended routine. The gym classifies a member’s performance as optimal if they follow the recommended routine for the six months, or as inferior otherwise. According to the historical results of the survey, 84% of the members with a low effort routine, 22% of the members with a medium effort routine, and 69% of the members with a high effort routine report optimal performance.
After the first six months of joining the gym, a member can obtain different results: they can either achieve their fitness goals, not achieve their goals, or have ended their membership. The gym has the following information about the fitness outcomes:
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96% of members with optimal performance and a high effort routine achieve their goals, the remaining 4% do not achieve them.
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6% of members with optimal performance and a medium effort routine do not achieve their goals, and 8% end their membership.
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7% of members with optimal performance and a low effort routine end their membership, and 9% do not achieve their goals.
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12% of members with inferior performance and a medium effort routine end their membership, and 18% do not achieve their goals.
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18% of members with inferior performance and a low effort routine end their membership, and 34% do not achieve their goals.
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4% of members with inferior performance and a high effort routine end their membership, and 14% do not achieve their goals.
Using this information,
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a) Draw the tree diagram that represents this situation (including percentages)
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