SOLUTION: If a poll percent in within 3% of the true percent p, and the poll percent is 31%, describe the possible values of p: a. using a double inequality; b. using absolute value.

Question 1199962: If a poll percent in within 3% of the true percent p, and the poll percent is 31%, describe the possible values of p:
a. using a double inequality;
b. using absolute value.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the poll percent is 31%.
the true percent is p.

a. using a double inequality.

p = 31% plus or minus 3%.
this tells you that p will be between 28% and 34%.

b. using absolute value.

absolute value of (31% - p) = 3%
if (31% - p) is positive, you get (31% - p) = 3%.
solve for p to get p = 31% - 3% = 28%
if (31% - p) is negative, you get -(31% - p) = 3% which becomes -31% + p = 3%.
solve for p to get p = 3% + 31% = 34%
this tells you that p will be between 28% and 34%.

the reason for this is because the absolute value of the expression has to be positive.
if it is positive, then the absolute value of it is already positive.
if it is negative, then the absolute value of it is multiplied by -1 to make it positive.
example:
the absolute value of 5 is equal to 5.
the absolute value of -5 is equal to -(-5) which is equal to 5.

RELATED QUESTIONS
In 2013, Gallup conducted a poll and found a 95% confidence interval of 52% < p < 60%,... (answered by Boreal)

A poll reported that 48% of residents opposed a new stadium. The poll was accurate to... (answered by stanbon)

if 37 of people in a poll hate KaBlamo juice, and thus constitutes 30% of the people in... (answered by advanced_Learner)

A recent poll of 380 randomly selected Americans showed that 24% ( = 0.24) are happy... (answered by stanbon)

One poll reported that 42% of city residents were against building a new civic center.... (answered by stanbon)

In a poll for the upcoming mayoral election, 42% of likely voters said they planned to... (answered by jim_thompson5910)

a) A poll of 2,295 likely voters was conducted on the president’s performance.... (answered by Boreal)

Aresearch institute poll asked respondents if they felt vulnerable to identity theft. In... (answered by Boreal)

Translate to a proportion: What percent of 45 is 62? Let p=the... (answered by ikleyn)