Final answer:
The clearance required for a front approach, push side door depends on the size and shape of the object or space being accommodated. For an aircraft doorway, the clearance would be based on the dimensions of the door and the average height and width of the passengers. Both parts (a) and (b) of the question are relevant for engineers designing the 757 aircraft.
Step-by-step explanation:
The clearance required for a front approach, push side door is typically determined by the size and shape of the object or space it needs to accommodate. In the case of an aircraft doorway, the clearance needed would depend on the dimensions of the door and the average height and width of the passengers who will be using it.
According to the information provided, for an aircraft door that needs to accommodate 95 percent of men without them needing to bend, the mean doorway height would need to be determined. The given data does not directly provide the mean doorway height, but it suggests using a rule of thumb that allows 95 percent of men to comfortably enter without bending.
For engineers designing the 757 aircraft, both results from parts (a) and (b) would be relevant. Part (a) provides the mean doorway height allowing 95 percent of men to enter without bending, which ensures that the majority of male passengers can comfortably enter. Part (b) considers the proportion of male passengers in the aircraft and provides the mean doorway height needed to satisfy a 0.95 probability that this height is greater than the mean height of 100 men. This result takes into account the specific passenger demographic of the aircraft.