Electricity bills: According to a government energy agency, the mean monthly household electricity bill in the United States in  2011  was  $108.87 . Assume the amounts are normally distributed with standard deviation  $18.00 . Use the TI-84 Plus calculator to answer the following. (a) What proportion of bills are greater than  $134 ? (b) What proportion of bills are between  $83  and  $145 ? (c) What is the probability that a randomly selected household had a monthly bill less than  $118 ? Round the answers to at least four decimal places.   Part 1 of 3       The proportion of bills that are greater than  $134  is    .         Part 2 of 3       The proportion of bills that are between  $83  and  $145  is   .         Part 3 of 3       The probability that a randomly selected household had a monthly bill less than  $118  is    .

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 + ...