To find the mean of the sampling distribution for the difference in the mean times (denoted as [tex]\(\bar{x}_A - \bar{x}_C\)[/tex]) between Alex and Chris, we can follow these steps:
1. Identify the population means for both Alex and Chris:
- The mean time for Alex is [tex]\(\mu_A = 5.28\)[/tex] minutes.
- The mean time for Chris is [tex]\(\mu_C = 5.45\)[/tex] minutes.
2. The mean of the sampling distribution for the difference in means is given by the difference in the population means:
[tex]\[
\mu_{\bar{X}_A - \bar{X}_C} = \mu_A - \mu_C
\][/tex]
3. Substitute the values of [tex]\(\mu_A\)[/tex] and [tex]\(\mu_C\)[/tex] into the formula:
[tex]\[
\mu_{\bar{X}_A - \bar{X}_C} = 5.28 - 5.45
\][/tex]
4. Calculate the difference:
[tex]\[
5.28 - 5.45 = -0.17
\][/tex]
Therefore, the mean of the sampling distribution for [tex]\(\bar{x}_A - \bar{x}_C\)[/tex] is [tex]\(-0.17\)[/tex].
So, the correct answer is [tex]\(\boxed{-0.17}\)[/tex].
