# A local firm manufactures LED products that have a lifespan that is approximately normally distributed with a std. dev. of 30 hours. If a sample of 30 LED products has an average lifespan of 780 hours, find a 96\% confidence interval for the population mean of all LED products produced by this firm.

A local firm manufactures LED products that have a lifespan that is approximately normally distributed with a std. dev. of 30 hours. If a sample of 30 LED products has an average lifespan of 780 hours, find a $96\mathrm{%}$ confidence interval for the population mean of all LED products produced by this firm.
Choose 2 answers in nearest unit (ones) or in whole number.
Example, if your answer is $888.83\le \mu \le 899.56$, choose 889 and 900.
$\begin{array}{|cccccccccccc|}\hline 775& 773& 807& 797& 791& 769& 789& 768& 805& 763& 771& 792\\ \hline\end{array}$

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Step 1
It is given that, and $\sigma =30$
At $96\mathrm{%}$ significance level, the value of z is 2.0537.
Then, the $96\mathrm{%}$ confidence interval is
$\stackrel{―}{x}±z\left(\frac{\sigma }{\sqrt{n}}=780±2.0537\left(\frac{30}{\sqrt{30}}\right)$
$=780±2.0537\left(5.4772\right)$
$=780±11.2486$

Rounded
Step 2
Therefore, 769 and 791 are the correct options.