For the following problem, you will need formulas for binomial experiments. n = the number of independent trials x = the number of successes in n trials 5 = success F = fail p = P(S) = probability of success in one trial q = 1 -p = PlF) P(x) = probability of x successes in n trials. The binomial probabilities are computed with the formula below. The form the binomial distribution: P(.'L') = 1103: -pm - qn'm. In this formula, an is computed using the special function on your calculator, which evaluates with this formula: 71.! n03: = m!(n * m)! . The mean of the binomial random variable, x, is: ,u. = E(m) = rip. The standard deviation of the binomial random variable is: 0' = , Mpg. Assume that 72.0% of the of U.S. adults are vaccinated from COVID 19. Next, assume that 6 U.S. adults are randomly selected, and that x is the number of these who are vaccinated. Enter the binomial probability distribution in the table below, rounded to 2 places after the decimal. In this series of questions, we will explore the center, shape, and spread of a sum of two random variables. We have learned that Elev + y) = EOE) + Eta) and if x and y are independent: Va'r($ + y) = Var(:r:) + Var(y). In this activity, you will need to compute population standard deviations and variances. In Desmos, enter data values as A = [ list of values ]. A = [list of values]. For the mean, use: mean(A). For the population standard deviation, use: stdevprA). For the population variance, use: stdevp(A)2. A population of values called x has the following values: {5, 6, 6, 7}. Give the population mean and variance of x below. (To compute the variance, square the unrounded population standard deviation. If you are very precise it will have only one place after the decimal.) p. = Eon) = S Va'r(a:) = a: = [:] For the following problem, you will need formulas for binomial experiments. n = the number of independent trials x = the number of successes in n trials 5 = success F = fail p = P(S) = probability of success in one trial q = 1 - p = P(F) P(x) = probability of x successes in n trials. The binomial probabilities are computed with the formula below. The form the binomial distribution: P(:1:) = nCm -pm - (flw. In this formula, an is computed using the special function on your calculator, which evaluates with this formula: n! C = . n a: m!(nm)l The mean of the binomial random variable, x, is: ,u. = E(:c) = up. The standard deviation of the binomial random variable is: 0' = 1Mpg. Assume that 40.0% of U.S. voters are registered as Independent. Next, assume that 8 U.S. voters are randomly selected, and that x is the number of these who are registered Independent. Enter the binomial probability distribution in the table below, rounded to 2 places after the decimal