An elevator has a placard stating that the maximum capacity is 2430 lb-15 passengers. So, 15 adult male passengers can have a mean weight of up to 2430/ 15 = 162 pounds. If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 162 lb. (Assume that weights of males are normally distributed with a mean of 171 Ib and a standard deviation of 32 lb.) Does this elevator appear to be safe? The probability the elevator is overloaded is. (Round to four decimal places as needed.) Does this elevator appear to be safe? O A. Yes, 15 randomly selected people will always be under the weight limit. O B. No, 15 randomly selected people will never be under the weight limit. O C. No, there is a good chance that 15 randomly selected people will exceed the elevator capacity. O D. Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity.

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### Educational Text on Elevator Capacity and Probability

An elevator has a placard stating that the maximum capacity is 2430 lb for 15 passengers. Therefore, 15 adult male passengers can have a mean weight of up to 2430 / 15 = 162 pounds. If the elevator is loaded with 15 adult male passengers, the task is to find the probability that it is overloaded because they have a mean weight greater than 162 lb. It is assumed that weights of males are normally distributed with a mean of 171 lb and a standard deviation of 32 lb. Does this elevator appear to be safe?

**The probability the elevator is overloaded is:** [ ].  
*(Round to four decimal places as needed.)*

#### Does this elevator appear to be safe?
- **A. Yes, 15 randomly selected people will always be under the weight limit.**
- **B. No, 15 randomly selected people will never be under the weight limit.**
- **C. No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.**
- **D. Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity.** 

#### Explanation:
- This question involves the understanding of normal distribution and probability.
- You need to calculate the probability that a random sample of 15 people will have a mean weight exceeding the elevator’s weight limit.
- The normal distribution information provided (mean = 171 lb, standard deviation = 32 lb) should be used to find the likelihood of exceeding the mean weight threshold of 162 lb.
Transcribed Image Text:### Educational Text on Elevator Capacity and Probability An elevator has a placard stating that the maximum capacity is 2430 lb for 15 passengers. Therefore, 15 adult male passengers can have a mean weight of up to 2430 / 15 = 162 pounds. If the elevator is loaded with 15 adult male passengers, the task is to find the probability that it is overloaded because they have a mean weight greater than 162 lb. It is assumed that weights of males are normally distributed with a mean of 171 lb and a standard deviation of 32 lb. Does this elevator appear to be safe? **The probability the elevator is overloaded is:** [ ]. *(Round to four decimal places as needed.)* #### Does this elevator appear to be safe? - **A. Yes, 15 randomly selected people will always be under the weight limit.** - **B. No, 15 randomly selected people will never be under the weight limit.** - **C. No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.** - **D. Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity.** #### Explanation: - This question involves the understanding of normal distribution and probability. - You need to calculate the probability that a random sample of 15 people will have a mean weight exceeding the elevator’s weight limit. - The normal distribution information provided (mean = 171 lb, standard deviation = 32 lb) should be used to find the likelihood of exceeding the mean weight threshold of 162 lb.
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