any Aplia problems use the following Distributions tool. You can use this tool to retrieve the information that you would get from a distributions table. The advantage of the tool is that it allows you to see in two dimensions how changing parameters, such as the z-score, will affect the resulting probabilities. Use the tool to complete the following table.    z Body Tail Mean to z       z Body Tail Mean to z 0.25 0.5987 0.4013 0.0987       1.55 0.9394 0.0606 0.4394 0.75                      2.15 0.9842 0.0158 0.4842 1.10 0.8643 0.1357 0.3643       2.65                1.30 0.9032 0.0968 0.4032       2.80 0.9974 0.0026 0.4974   To find the probability of a z-score, position the orange line at the appropriate z-score on the horizontal axis. The areas under the standard normal curve to the left and right of the vertical line are displayed in blue and orange, respectively. (Hint: The standard normal distribution is symmetrical about the mean, the area under the curve to the left (and right) of the mean is 0.5. Therefore, the area that corresponds with Mean to z is computed as Larger Portion (Body or Tail) – 0.5.)   Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0   -3.00-2.50-2.00-1.50-1.00-0.500.000.501.001.502.002.503.00z.5000.50000.000     Grade It Now Save & Continue

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 + ...