Algebra public opinion polls reported in newspapers are usually given with a margin of error. for example, a poll with a margin of error of ±5% is considered accurate to within plus or minus 5% of the actual value. a poll with a stated margin of error of 6.3% predicts that candidate towne will receive 51% of an upcoming vote. write and solve an equation describing the minimum and maximum percent of the vote that candidate towne is expected to receive.

Question

Ari Valentine

Mathematics

10 September, 19:14

Algebra public opinion polls reported in newspapers are usually given with a margin of error. for example, a poll with a margin of error of ±5% is considered accurate to within plus or minus 5% of the actual value. a poll with a stated margin of error of 6.3% predicts that candidate towne will receive 51% of an upcoming vote. write and solve an equation describing the minimum and maximum percent of the vote that candidate towne is expected to receive.

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Diya · Answer 1

Minimum percent of the vote that candidate Towne is expected to recieve:

m=51% - 6.3% * 51% = 47.787%

Maximum percent of the vote that candidate Towne is expected to recieve:

M=51% + 6.3% * 51% = 54.213%

Solution:

Margin of error: E=6.3%

Minimum percent of the vote that candidate Towne is expected to recieve:

m=51% - E * 51%

m=51% - 6.3% * 51%

m=51% - 51% * 6.3 / 100

m=51% - 3.213%

m=47.787%

Maximum percent of the vote that candidate Towne is expected to recieve:

M=51% + E * 51%

M=51% + 6.3% * 51%

M=51% + 51% * 6.3 / 100

M=51% + 3.213%

M=54.213%