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Answer :
The elevator has a maximum capacity of 1248 pounds or 8 passengers. To determine if the elevator is safe, we need to consider the weight of 8 randomly selected adult male passengers.
The mean weight of adult male passengers is 161 pounds, with a standard deviation of 27 pounds. Since the weights of adult males are normally distributed, we can use this information to calculate the probability that the elevator is overloaded.
To find the probability, we first need to calculate the mean weight of 8 randomly selected adult male passengers. We divide the maximum capacity by the number of passengers: 1248 pounds / 8 passengers = 156 pounds.
Next, we need to calculate the standard deviation of the mean weight of the 8 passengers. Since we are randomly selecting passengers, the standard deviation of the mean weight can be calculated by dividing the standard deviation of individual weights by the square root of the number of passengers: 27 pounds / sqrt(8) = 9.55 pounds (rounded to two decimal places).
Now, we can use the normal distribution to find the probability that the mean weight of 8 randomly selected adult male passengers exceeds the maximum capacity of 156 pounds. We will calculate the z-score, which is the number of standard deviations the mean weight is above the maximum capacity.
Using the formula z = (x - μ) / σ, where x is the maximum capacity (156 pounds), μ is the mean weight (161 pounds), and σ is the standard deviation of the mean weight (9.55 pounds), we can calculate the z-score.
z = (156 - 161) / 9.55 ≈ -0.52
Using a standard normal distribution table or calculator, we find that the probability of a z-score of -0.52 or lower is approximately 0.3015.
Therefore, the probability that the elevator is overloaded with 8 randomly selected adult male passengers is 0.3015.
To determine if the elevator is safe, we compare this probability to a threshold. If the probability is below the threshold (e.g., 0.05), then the elevator appears to be safe. If the probability is above the threshold, then there is a higher chance that 8 randomly selected adult male passengers will exceed the elevator capacity.
In this case, since the probability of overloading the elevator is 0.3015, which is greater than 0.05, we can conclude that the elevator does not appear to be safe. Therefore, the correct answer is A. No, there is a good chance that 8 randomly selected adult male passengers will exceed the elevator capacity.
To know more about standard deviation here:
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