Finding the Mean, Variance, and Standard Deviation of a Binomial Distribution About 8% of the population has a particular genetic mutation. Suppose 1000 people are randomly selected and the number with the particular genetic mutation are counted. 1) Find the mean number of people who will have the genetic mutation in such groups of 1000 people.    2) Find the variance of the number of people who will have the genetic mutation in such groups of 1000 people. Round answer to 2 decimal places.    3) Find the standard deviation of number of people who will have the genetic mutation in such groups of 1000 people. Round answer to 2 decimal places.

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 + ...