Mathematics, 20.01.2020 21:31 person779

In a recent survey of 25 voters, 17 favor a new city regulation and 8 oppose it. what is the probability that in a random sample of 6 respondents from this survey, exactly 2 favor the proposed regulation and 4 oppose it?

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Answer from: 3peak101

$P(X=2)=(6C2)(0.68)^2 (1-0.68)^{6-2}=0.0727$

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

The probability in favor of the regulation based on the recent survey is:

$p = \frac{17}{25}=0.68$

Let X the random variable of interest "Number of favor respondents about the regulation", on this case we now that:

$X \sim Binom(n=6, p=0.68)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X=2)=(6C2)(0.68)^2 (1-0.68)^{6-2}=0.0727$

If we use X= "Number of respondednts opposed to the regulation we got the same answer", but on this case p = 1-0.68=0.32, and we want this probability:

$P(X=4)=(6C4)(0.32)^4 (1-0.32)^{6-4}=0.0727$

Answer from: Quest

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

Answer from: Quest

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

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In a recent survey of 25 voters, 17 favor a new city regulation and 8 oppose it. what is the probabi...

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