The margin of error for a 95% confidence interval is 0.263.
<h3>What is normal distribution?</h3>
A probability distribution which is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
- The probability bell curve is more properly described as the normal distribution.
- The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has an outlier of 3 and zero skew.
- Not everyone symmetrical distributions are normal, but all normal distributions are symmetrical.
The formula for margin of error is ;
ME = (z × σ) / √ n
The confidence interval is 95% = 0.95.
Mean (σ) =14
standard deviation = 3.
Total population (n) = 500
Substitute the values in the formula;
ME = (z × σ) / √ n
= (1.96 × 3)/√500
= (1.96 × 3)/22.36
ME = 0.263
Therefore, the margin of error for a 95% confidence interval is 0.263.
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The complete question is -
A study of five hundred adults found that the number of hours they spend on social networking sites each week is normally distributed with a mean of 14 hours. The population standard deviation is 3 hours. What is the margin of error for a 95% confidence interval?
