# Part II: Discrete Variables and their Distributions, (Read Hints below) 3. A certain disease has an infection rate 1/5 in a rural area of 40 people.

Part II: Discrete Variables and their Distributions,(Read Hints below)3. A certain disease has an infection rate 1/5 in a rural area of 40 people. A sample of size 10 is taken at random without replacement. Let X be the number of infected people in the sample. (1) What is the distribution of X? Give the name of the distribution and values of the parameters; (2) List all the possible values of X;(3) Find the probability that exactly 2 individuals in the sample are infected by the disease;and variance 2 of X using the formulas for this distribution;(5) Explain the formula for ; (6) Interpret the probability you calculated in (3).Have to show all work toAbout Binomial and HyperGeometric Distributions: If trials are independent (or approximately independent), the resulting distribution is Binomial; otherwise, it is HyperGeometric.For HyperGeometric distribution, the formulas for the mean and variance are