Question

Central Limit Theorem application:

In product design for human use and recommended guideline for the product’s human use, it is important to consider the weights of people so that airplanes or elevators aren’t overloaded. Based on data from the National Health Survey, the weight of adults in the United States has a mean of 181 pound (the average of 195.5 for males and 166.2 for females, assuming, arbitrarily, equal male and female population) with a standard deviation of 30 pounds. An airplane is designed to have a human carrying maximum-capacity 18,500 pounds. An Airline adopts the operation procedure of maximum passenger number (n), based on the concept of the probability of a randomly selected n passengers exceeding the maximum-capacity to be less than 0.01 (i.e., 1%).

1. [3 pts] Determine n
2. [2 pts] What will be the value of n if the probability of exceeding the maximum-capacity is no more than 0.001 (i.e., 0.1%)?

Answer 1