There are 20 crew members at a given university. You want to calculate the probability that their mean BMI will be 2 units below the mean BMI for the population. Assume the standard deviation is 5 and the outcome is normally distributed in the population.  Hint: you have all of the information you need to calculate the answer to this question. Ask yourself, what is the value of the numerator? If it helps, substitute (made up) numbers for the variables in the numerator based on the information given in the question.  Which probability model should you apply to this question, and why?  Calculate the probability.

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 + ...