The workers' union at a particular 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 5 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members?Round your response to at least three decimal places. (If necessary, consult a list of formulas.)
Question
The workers' union at a particular 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 5 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members?Round your response to at least three decimal places. (If necessary, consult a list of formulas.)
Solution
This problem can be solved using the binomial probability formula, which is:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success on a single trial
- n is the number of trials
- k is the number of successes
In this case:
- n = 5 (the number of workers interviewed)
- k = 2 (the number of union members we're interested in)
- p = 0.94 (the probability that a worker chosen at random is a union member)
First, calculate C(n, k), which is the number of combinations of 5 items taken 2 at a time. This can be calculated as:
C(n, k) = n! / [k!(n-k)!] = 5! / [2!(5-2)!] = 10
Next, calculate p^k, which is (0.94)^2 = 0.8836
Then, calculate (1-p)^(n-k), which is (0.06)^3 = 0.000216
Finally, multiply these three values together to get the probability:
P(X=2) = C(n, k) * (p^k) * ((1-p)^(n-k)) = 10 * 0.8836 * 0.000216 = 0.00191
So, the probability that exactly 2 of the workers interviewed are union members is approximately 0.002, or 0.2%.
Similar Questions
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 20 workers, chosen at random, to get their opinions on the strike.Answer the following.
A union spokesperson claims that 75% of union members will support a strike if their basic demands are not met. A company negotiator believes the true percentage is lower and runs a hypothesis test. What is the conclusion if 87 out of a simple random sample of 125 union members say they will strike?For each of the two possible answers above, what error might have been committed, Type I or Type II, and what would be a possible consequence?
A survey of professions had the results shown in the table. What is the probability that a person chosen at random from the survey respondents would work in health care? Round your answer to three decimal places.Retail 42Health Care 70Food 107Physical Labor 67Office Work 106Agriculture 54Group of answer choicesNot enough information to calculate.0.1576.3710.094
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.
Question 2In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. You are going to select an individual from the group of students. The probability of event A is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. What is the probability of the event A’s complement?1 point0.510.260.490.74
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.