Human pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days.  The shortest 2% of pregnancies result in babies that are considered clinically premature.  What number of days of pregnancy or less corresponds to the birth of a premature baby?  Are you calculating the top or bottom 2%? Answer So, which percentage needs to be converted to an area? Answer What is the area that you will look for in the table (four decimal places)? Answer What area will you actually use from the table (four decimal places)? Answer What is the z-score associated with that area (two decimal places)? Answer What is the cutoff number of days that corresponds to the shortest 2% of pregnancies? (round to the nearest whole number)   Answerdays Are values lower or higher than that value also in the shortest 2%?

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 + ...