A car manufacturer tested the gap between the doors and the body of a new car using $18$ samples in millimeters as shown: $1\mathrm{.}7,1\mathrm{.}9,1\mathrm{.}4,1\mathrm{.}4,1\mathrm{.}5,1\mathrm{.}7,1\mathrm{.}1,1\mathrm{.}6,1\mathrm{.}9,1\mathrm{.}4,1\mathrm{.}5,1\mathrm{.}5,1\mathrm{.}6,1\mathrm{.}5,1\mathrm{.}3,1\mathrm{.}8,1\mathrm{.}6,$ and $1\mathrm{.}2.$

a$)$ Determine the sample mean and standard deviation. $\frac{K}{U}-4$

b$)$ Calculate the z$-$score of a door with a gap of $1\mathrm{.}7mm$ and explain the result. $A-1,C-1$

c$)$ Calculate the z$-$score of a door with a gap of $1\mathrm{.}1mm$ and explain the result. $A-1,C-1$

$+$

d$)$ The manufacturer rejects any cars with door gaps that are not within two standard deviations of the mean. Which cars would be rejected? $[$T$/$I $-2]$