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In a survey of 1467 people, 1021 people voted











































Probability that at least 1021 did vote

In a survey of 1467 people, 1021 people said they voted in a recent election.


Voting records show that 67% of the eligible voters actually did vote.


Given that 67% of the voter actually did vote:


Find the probability that among 1467 randomly selected voters, at least 1021 actually did vote.

Comments for In a survey of 1467 people, 1021 people voted

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Nov 10, 2012
Probability of Voting
by: Staff


Answer

Part I

p = proportion of voters in the population (number of voters, X, divided by the entire population, N)

p = x/n

p = .67 (from the problem statement)


q = proportion of non-voters in the population (1 minus p)

q = 1 - p

q = 1 - 0.67

q = 0.33

μ = what the number of voters in our sample should be, based the known population proportion

μ = np = 1467(.67) ≈ 982.89. In other words, since we already know that 67% of the population voted, the results of our sample should show that 982.89 people in our sample voted.

σ² = variance of our sample based on population proportion of 67% voters

σ² = npq = 1467(.67)(.33) = 324.354

σ = standard deviation of our sample based on the population proportion of 67 % voters

σ = √(σ²)

σ = √(324.354)

σ ≈ 18.0098

z = z score, the number of standard deviations our sample voter statistic of 1021 voters is from the expected mean of 982.89 voters

z = (x̄ - μ) / σ

z = (1021 - 982.89) / 18.0098 ≈ 2.11607

P(z ≥ 2.11607) = 1.70% (this is the purple area under the curve shown below)

Once you know the z-score (which is 2.11607) you can calculate the percentage that at least 1021 did vote by using a calculator or a z table.



Math – graph of  y = (3x + 5)




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Nov 10, 2012
Probability of Voting
by: Staff

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Part II

(remember that the answer to your question (when z is 2.11607) is the area under the right hand tail of the curve, from z = 2.11607 and upward)

P(z ≥ 2.11607)= 1 - (value calculated by most calculators) = 1.70%

A good on-line statistics calculator can be found at:

http://www.danielsoper.com/statcalc3/calc.aspx?id=2


A downloadable z-table can be found at:

http://www.doe.virginia.gov/testing/test_administration/ancilliary_materials/mathematics/2009/2009_sol_z_table.pdf



Final Answer:


                 1.70%





Thanks for writing.

Staff
www.solving-math-problems.com



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