$($b$)$ Considering only offices with a wait tracking system, what is the $z-$score for the sixth patient in the sample $($wait time $=38)?$ How does this $z-$score compare with the $z-$score you calculated for part $(a)?$

We will again use the STANDARDIZE function in Excel to determine this $z-$score. As before, first calculate the sample mean and sample standard deviation of the data. Since these formulas were already determined for the data in column B$,$ each can be copied and pasted to cells C$12$ and C$13,$ respectively. Doing so gives the following mean and standard deviation, rounded to three decimal places.

$\backslash$table$[[,$A$,$B$,$C$,$D$],[1,$Patient Number,Without Tracking,With Tracking,z$-$score without tracking$],[2,1,23,32,],[3,2,66,12,],[4,3,16,15,],[5,4,19,19,],[6,5,32,11,],[7,6,45,38,],[8,7,13,8,],[9,8,24,14,],[10,9,15,11,],[11,10,38,16,0\mathrm{.}53],[12,$Mean,$29\mathrm{.}1,17\mathrm{.}6,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}},],[13,$Standard Deviation,$16\mathrm{.}656,9\mathrm{.}264,x,],[14,,,,,]]$