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Answer :
The answer is: C. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity. To find the probability that the elevator is overloaded, we need to calculate the probability that the mean weight of the 12 adult male passengers exceeds 176 pounds.
We know that the weights of the passengers are normally distributed with a mean of 178 pounds and a standard deviation of 29 pounds. The mean weight of 176 pounds is below the mean weight of the population.
To find the probability, we need to standardize the mean weight of 176 pounds using the formula:
Z = (X - μ) / σ
Where X is the mean weight, μ is the population mean, and σ is the population standard deviation.
Substituting the values, we have:
Z = (176 - 178) / 29
Z = -0.069
Next, we need to find the probability that the standardized mean weight is greater than -0.069.
We can look up this probability in the standard normal distribution table or use a calculator.
Using the standard normal distribution table, we find that the probability of Z being greater than -0.069 is approximately 0.5279.
Therefore, the probability that the elevator is overloaded because the mean weight of the 12 adult male passengers exceeds 176 pounds is approximately 0.5279.
Based on this probability, we can conclude that there is a good chance that 12 randomly selected people will not exceed the elevator capacity.
Therefore, the answer is: C. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity.
The elevator appears to be safe.
This means that the elevator is likely to be able to handle the weight of 12 randomly selected adult male passengers without being overloaded.
For more information on probability visit:
brainly.com/question/32117953
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