Answer :
Final Answer:
The capacity of the elevator will be exceeded if the mean weight of the 12 people is greater than 172 pounds.
Explanation:
Given data:
Mean weight (μ) = 170 pounds
Standard deviation (σ) = 10 pounds
Sample size (n) = 12
To determine if the capacity will be exceeded, we calculate the mean weight of the 12 people:
Mean weight per person = μ = 170 pounds
Now, calculate the mean weight of all 12 people:
Mean weight of 12 people = μ_total = n * μ = 12 * 170 = 2040 pounds
Since the mean weight exceeds the threshold for capacity (2064 pounds), which is equivalent to 172 pounds per person, the capacity of the elevator will be exceeded if the mean weight of the 12 people is greater than 172 pounds.