In your role as a quality control analyst at ABC Manufacturing, you are examining theproduction quality of brake pads. It is critical to maintain stringent quality control to ensurethe product meets the required specifications $(5\mathrm{.}0$ mm to $6\mathrm{.}0$ mm$).$ Over a $10-$hour shift, youhave recorded the thickness of brake pads each hour, resulting in the data presented in Table$1.$ You suspect that there may be fluctuations in the production process and need to analysethe data to confirm process stability.

Table $1$: The thickness of brake pads recorded

over a $10-$hour period

$($a$)$

Describe three scenarios where using a histogram would be appropriate for analysing thebrake pad thickness data.

$(5)$

$($b$)$

Construct a histogram using the brake pad thickness data provided. Clearly show yourcalculations for determining the number of classes, class width, and class intervals.

$(10)$

$($c$)$

Analyse the histogram you constructed and determine if the brake pad thicknessdistribution meets the quality standards specified $(5\mathrm{.}0$ mm to $6\mathrm{.}0$ mm$).$ Discuss anypotential issues that the histogram reveals.

$($