Introduction:

a) Confidence interval formula for the population mean is given by

\(\displaystyle{C}.{I}=\overline{{{x}}}\pm{z}_{{{\frac{{\alpha}}{{{2}}}}}}{\frac{{{s}{d}}}{{\sqrt{{{n}}}}}}\)

where x-bar is the sample mean

\(\displaystyle{z}_{{{\frac{{\alpha}}{{{2}}}}}}\) - is the critical value

\(\displaystyle{s}{d}\) - is the sample standard deviation

\(\displaystyle{n}\) - is sample size.

b) Confidence interval formula for the population standard deviation is given by

\(\displaystyle{C}.{I}={\frac{{{\left({n}-{1}\right)}{s}^{{{2}}}}}{{{\chi_{{{\frac{{\alpha}}{{{2}}}}}}^{{{2}}}}}}}{ < }\sigma^{{{2}}}{ < }{\frac{{{\left({n}-{1}\right)}{s}^{{{2}}}}}{{{\chi_{{{1}-{\frac{{\alpha}}{{{2}}}}}}^{{{2}}}}}}}\)

Here n is sample size

\(\displaystyle{s}^{{{2}}}\) - is the sample variance

\(\displaystyle{\chi_{{{\frac{{\alpha}}{{{2}}}}}}^{{{2}}}}\) - is the critical value

\(\displaystyle{n}\) - is the sample size

Step 2

Part 1: Normal probability plot

From the above normal probability plot we can observe that the given set of data follows normal distribution.Since, the all the data points are close to each other and to wards the straight line. Further, it confirms that the number of hours that the LED lights of this brand worked following normality.