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The margin of error for 324 adults surveyed with 1.6 standard deviations is 0.1742.
<h3>What is the margin of error?</h3>The margin of error can be defined as the amount of random sampling error in the results of a survey. It is given by the formula,
= margin of error
= confidence level
= quantile
σ = standard deviation
n = sample size
As it is given that the sample size of the survey is 324, while the standard deviation of the survey is 1.6.
We know that the value of the z for 95% confidence interval is 1.96. Therefore, using the formula of the standard of error we can write it as,
Hence, the margin of error for 324 adults surveyed with 1.6 standard deviations is 0.1742.
Learn more about Margin of Error:
The absolute value function |<em>x</em>| always returns a non-negative number. It takes any number <em>x</em> and returns <em>x</em> if it's already non-negative, or -<em>x</em> if it is negative in order to make it positive.
For the equation
-3 + 4 |2<em>x</em> - 5| = 14
rearrange terms to get
|2<em>x</em> - 5| = 17/4
Now,
• if 2<em>x</em> - 5 ≥ 0, then |2<em>x</em> - 5| = 2<em>x</em> - 5. Then
2<em>x</em> - 5 = 17/4
• and if instead 2<em>x</em> - 5 < 0, then |2<em>x</em> - 5| = -(2<em>x</em> - 5), so that
-(2<em>x</em> - 5) = 17/4, or
2<em>x</em> - 5 = -17/4
In the first case,
2<em>x</em> - 5 = 17/4
2<em>x</em> = 17/4 + 5 = 37/4
<em>x</em> = 37/8
In the second case,
2<em>x</em> - 5 = -17/4
2<em>x</em> = -17/4 + 5 = 3/4
<em>x</em> = 3/8