Question

The mean for a set of measurements is 4.17 and the standard deviation is 0.14. To show 95% confidence limits, we can write the result of the measurements as 4.17+ -

Answer 1

Answer:

The 95% confidence level is

$4.17 \pm 0.2744$

Explanation:

If we can apply the central limit theorem, we can approximate this distribution to a normal distribution.

The confidence level (for n=1) is defined as

$X\pm \frac{z*\sigma}{\sqrt{n}}=X\pm z*\sigma$

For a 95% confidence interval, according to the normal distribution, z=1.96.

Then we have:

$X\pm z*\sigma=4.17 \pm 1.96*0.14=4.17 \pm 0.2744$