the workers union at a certain university is quite strong. about 94% of all workers employed by the…

the workers union at a certain university is quite strong. about 94% of all workers employed by the university belong to the workers union. recently, the workers went on strike, and now a local tv station plans to interview a sample of 10 workers, chosen at random, to get their opinions on the strike. answer the following. (if necessary, consult a list of formulas.) (a) estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). do not round your response. (b) quantify the uncertainty of your estimate by giving the standard deviation of the distribution. round your response to at least three decimal places.

the workers union at a certain university is quite strong. about 94% of all workers employed by the university belong to the workers union. recently, the workers went on strike, and now a local tv station plans to interview a sample of 10 workers, chosen at random, to get their opinions on the strike. answer the following. (if necessary, consult a list of formulas.) (a) estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). do not round your response. (b) quantify the uncertainty of your estimate by giving the standard deviation of the distribution. round your response to at least three decimal places.

Answer

Explanation:

Step1: Identify the distribution

This is a binomial - distribution problem. Let (X) be the number of union - member workers in the sample. The binomial distribution has parameters (n) (number of trials) and (p) (probability of success in a single trial). Here, (n = 10) (the number of workers in the sample) and (p=0.94) (the probability that a worker is a union member).

Step2: Calculate the mean of the binomial distribution

The mean (expected value) of a binomial distribution (X\sim B(n,p)) is given by the formula (\mu = E(X)=np). Substitute (n = 10) and (p = 0.94) into the formula: (\mu=10\times0.94 = 9.4)

Step3: Calculate the standard deviation of the binomial distribution

The standard deviation of a binomial distribution (X\sim B(n,p)) is given by the formula (\sigma=\sqrt{np(1 - p)}). Substitute (n = 10), (p = 0.94), and (1-p=0.06) into the formula: (\sigma=\sqrt{10\times0.94\times0.06}=\sqrt{0.564}\approx0.751)

Answer:

(a) 9.4 (b) 0.751