High School

We appreciate your visit to There is an elevator with a maximum capacity of 4000 lb When rating elevators a 25 safety factor is typically used so the elevator should. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

There is an elevator with a maximum capacity of 4000 lb. When rating elevators, a 25% safety factor is typically used, so the elevator should actually be able to carry a load that is 25% greater than the stated limit. Thus, the maximum capacity of 4000 lb becomes 5000 lb after it is increased by 25%.

For 27 adult male passengers, the mean weight can be up to 185 lb.

If the elevator is loaded with 27 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 185 lb. Assume that the weights of males are normally distributed with a mean of 189 lb and a standard deviation of 39 lb.

Does this elevator appear to be safe?

Answer :

Final answer:

The probability that the elevator is overloaded because the mean weight of the 27 adult male passengers is greater than 185 lb is approximately 0.4582. The elevator appears to be safe.

Explanation:

To find the probability that the elevator is overloaded because the mean weight of the 27 adult male passengers is greater than 185 lb, we need to calculate the z-score and find the corresponding probability.

First, let's calculate the z-score using the formula:

z = (x - μ) / σ

where:

  • z is the z-score
  • x is the value we want to find the probability for (185 lb)
  • μ is the mean weight (189 lb)
  • σ is the standard deviation (39 lb)

Substituting the values into the formula, we get:

z = (185 - 189) / 39 = -0.1026

Next, we need to find the probability corresponding to this z-score. We can use a standard normal distribution table or a calculator to find the probability. In this case, the probability is approximately 0.4582.

Therefore, the probability that the elevator is overloaded because the mean weight of the 27 adult male passengers is greater than 185 lb is approximately 0.4582.

Now, let's determine if the elevator appears to be safe. Since the probability is less than 0.5 (50%), it is unlikely that the elevator will be overloaded due to the mean weight of the passengers. Therefore, the elevator appears to be safe.

Learn more about probability and statistics here:

https://brainly.com/question/27342429

#SPJ14

Thanks for taking the time to read There is an elevator with a maximum capacity of 4000 lb When rating elevators a 25 safety factor is typically used so the elevator should. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada