An elevator has a placard stating that the maximum capacity is 2016 lb—12 passengers.​ So, 12 adult male passengers can have a mean weight of up to 2016/12=168 pounds. If the elevator is loaded with 12 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb.​ (Assume that weights of males are normally distributed with a mean of 174 lb and a standard deviation of 25 lb​.) Does this elevator appear to be​ safe? The probability the elevator is overloaded is nothing. ​(Round to four decimal places as​ needed.) Does this elevator appear to be​ safe?   A.  YES, THERE IS A GOOD CHANCE THAT 12 RANDOMLY SELETECTED PEOPLE WILL NOT EXCEED THE ELEVATOR CAPACITY.    B. NO, 12 RANDOMLY SELECTED PEOPLE WILL NEVER BE UNDER THE WEIGHT LIMIT   C. NO, THERE IS A GOOD CHANCE THAT 12 RANDOMLY SELECTED ADULT MALE PASSENGERS WILL EXCEED THE ELEVATOR CAPACITY   D. YES, 12 RANDOMLY SELECTED ADULT MALE PASSENGERS WILL ALWAYD BE UNDER THE WEIGHT LIMIT

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...