High School

The capacity of an elevator is 12 people or 2,064 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than [tex] \frac{2064}{12} = 172 [/tex] pounds. Suppose the people have weights that are normally distributed with a mean of 170 pounds and a standard deviation of 10 pounds.

Determine the probability that the total weight of 12 people exceeds the elevator's capacity.

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.

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