The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4770 households discard waste with weights having a mean that exceeds 26.79 lb/wk. For many different weeks, it is found that the samples of 4770 households have weights that are normally distributed with a mean of 26.31 lb and a standard deviation of 12.64 lb. What is the proportion of weeks in which the waste disposal facility is overloaded? P(M > 26.79) =  Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. Is this an acceptable level, or should action be taken to correct a problem of an overloaded system? Yes, this is an acceptable level because it is unusual for the system to be overloaded. No, this is not an acceptable level because it is not unusual for the system to be overloaded.

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 + ...