$($a$)$ A highway utilising four lanes in each direction was studied to see whether drivers prefer to drive on the inside lanes. A total of $1000$ vehicles was observed during the heavy early$-$morning traffic and their respective lanes recorded. The results were as follows: Lane Count $294276238192($b$)$ Are some lanes preferred over others? $[10$ marks$]$ Part variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rapid wear$-$out. Production standards call for a maximum variance of $0\mathrm{.}0001$ when the bearing sizes are measured in inches. A sample of $15$ bearings shows a sample standard deviation of $0\mathrm{.}014$ inches. Determine whether the sample indicates that the maximum acceptable standard is being exceeded. $[10$ marks$)$