# 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

 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. ----------------------------------

 Nov 10, 2012 Probability of Voting by: Staff ---------------------------------- 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