Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ An elevator has a placard stating that the maximum capacity is 1256 lb for 8 passengers. So, 8 adult male passengers can have a mean weight of up to [tex]\frac{1256}{8} = 157[/tex] pounds.

If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb.

Assume that weights of males are normally distributed with a mean of 164 lb and a standard deviation of 28 lb.

Does this elevator appear to be safe?

The probability that the elevator is overloaded is ___.

To find the probability that the elevator is overloaded, we need to determine the probability that the mean weight of 8 passengers is greater than 157 lb.

We can use the Central Limit Theorem to approximate the distribution of the mean weight. The mean weight of 8 passengers is normally distributed with a mean of 164 lb and a standard deviation of 28 lb divided by the square root of 8 (since we're taking the mean of a sample size of 8).

By z-scoring the value of 157, we can find the corresponding area under the normal curve, which represents the probability that the mean weight is greater than 157 lb. Using a standard normal distribution table or a calculator, we find that the area to the right of the z-score is approximately 0.6064. Therefore, the probability that the elevator is overloaded is approximately 0.6064 or 60.64%.

Learn more about probability here:

https://brainly.com/question/22962752

#SPJ11