For 99.9% confidence, Z = 3.291

We have the mean value \overline{x} given as 9.84 s. The standard deviation s is given as 0.08mm. The number of randomly selected students is n = 8.

Substituting this in the formula \overline{x} \pm Z \frac{s}{\sqrt{n}}

we get 9.84\ \pm3.921\ \times\frac{0.08}{\sqrt{8}}

= 9.84\ \pm3.291\ \times\frac{0.08}{2.828..}

=\ 9.84\ \pm0.09\

So the population mean time of all the 100 m runners is almost certain to be between 9.75 s and 9.93 s.

So option C is the right answer.

I found an answer from www.statisticshowto.com

**Confidence Interval**: How to **Find** it: The Easy Way! - Statistics How To

How to **find** a **confidence interval** for a sample or proportion in easy **steps**. ... But in reality, most **confidence intervals** are found using the t-distribution (especially if you are ... **Step** 3: Look up your **answers** to **step** 1 and 2 in the t-distribution table. ... **Example question**: **Calculate** a 95% **confidence interval** for the true population ...

For more information, see **Confidence Interval**: How to **Find** it: The Easy Way! - Statistics How To