According to a health publication, 15.9% of persons under the age of 65 have no health insurance coverage. Suppose that four persons under the age of 65 are randomly selected. a. Determine the probability distribution for the number, X, who have no health insurance coverage. b. Determine and interpret the mean of X a. Complete the table below to determine the probability distribution of X. In this problem, you are calculating the probability value for each possible value of X. You will first calculate the probability that X equals 0. This calcualted probability will then go in the column next to 0. Then you will calculate the probability that X equals 1. This calculated probability will go in the column next to and so on. 2 3 4 (Round to four decimal places as needed.) b. The mean of X is Choose the correct interpretation of the mean below. O A. On average, we would expect this many people out of one under the age of 65 to have no health insurance coverage. 0 B. On average, we would expect this many people out of four under the age of 65 to have health insurance coverage ° C. On average, we would expect this many people out of four under the age of 65 to have no health insurance coverage

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 + ...