In a survey, 55% of the voters support a particular referendum. If 30 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.
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To find the standard deviation of the number of voters who support the referendum, we need to use the binomial distribution formula.
The binomial distribution formula is:
P(X = k) = (nCk) * p^k * q^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes in n trials
- nCk is the binomial coefficient, which represents the number of ways to choose k successes out of n trials
- p is the probability of success in a single trial
- q is the probability of failure in a single trial (q = 1 - p)
In this case, we know that 55% of voters support the referendum, which means p = 0.55. The probability of failure, q, is 1 - p, so q = 1 - 0.55 = 0.45.
We are asked to find the standard deviation of the number of voters who support the referendum. The formula for the standard deviation of a binomial distribution is:
σ = sqrt(n * p * q)
Where:
- σ is the standard deviation
- n is the number of trials (in this case, the number of voters chosen at random)
- p is the probability of success in a single trial
- q is the probability of failure in a single trial
In this case, the number of voters chosen at random is 30, so n = 30.
Now, we can plug in the values into the formula:
σ = sqrt(30 * 0.55 * 0.45)
Calculating this expression gives us the standard deviation of the number of voters who support the referendum.