Math 208 project
(1) What percentage of the population are we willing to exclude?
(2) How much extra room do we want to provide for passenger comfort and safety? Use the available information to determine the sitting distance. Identify the choices and decisions that were made in that determination.
Mean
Standard
Deviation Distribution
Males 23.5 in. 1.1 in. Normal
Females 22.7 in. 1.0 in. Normal
Part I- Answer:
In order for an airline company to be profitable, it has to differentiate itself from others by focusing on customers’ comfort and safety. That being said, an airline cannot satisfy everyone as well as it cannot accommodate everyone. It has to find the best strategy to maximize the number of passengers without compromising the comfort or safety levels.
First, we take a look at what percentage of the population the airline is willing to exclude and still not upset customers. The airline cannot afford to accommodate or satisfy 99% of the population. If the airline chose to set a fixed sitting distance like for example, 26 inches. Since men are taller than women from the table, we will only be considering men heights.
Z= (26-23.5)/1.1 = 2.27, which means that the airline is seating 98.8% of the people comfortably. From the passengers’ point of view, this could be a favorable solution. However, the airline has to be profitable and efficient at the same time. The airline can chose to satisfy 95% of the people. The company will still be able to satisfy a large portion of the population and can be profitable. We find the minimum/ maximum sitting distance for men/ women that will satisfy 95% of the people:
Because of the normal distribution the mean= 0, standard deviation=1.
95 percent means z= +/- 1.96
Max sitting distance for men = 23.5 +(1.96*1.1)= 25.656 inches
Min sitting distance for men = 23.5 -(1.96*1.1)= 21.344 inches
Max sitting distance for women= 22.7 +(1.96*1) = 24.66 inches
Min sitting distance for women = 22.7 -(1.96*1) =
(2) How much extra room do we want to provide for passenger comfort and safety? Use the available information to determine the sitting distance. Identify the choices and decisions that were made in that determination.
Mean
Standard
Deviation Distribution
Males 23.5 in. 1.1 in. Normal
Females 22.7 in. 1.0 in. Normal
Part I- Answer:
In order for an airline company to be profitable, it has to differentiate itself from others by focusing on customers’ comfort and safety. That being said, an airline cannot satisfy everyone as well as it cannot accommodate everyone. It has to find the best strategy to maximize the number of passengers without compromising the comfort or safety levels.
First, we take a look at what percentage of the population the airline is willing to exclude and still not upset customers. The airline cannot afford to accommodate or satisfy 99% of the population. If the airline chose to set a fixed sitting distance like for example, 26 inches. Since men are taller than women from the table, we will only be considering men heights.
Z= (26-23.5)/1.1 = 2.27, which means that the airline is seating 98.8% of the people comfortably. From the passengers’ point of view, this could be a favorable solution. However, the airline has to be profitable and efficient at the same time. The airline can chose to satisfy 95% of the people. The company will still be able to satisfy a large portion of the population and can be profitable. We find the minimum/ maximum sitting distance for men/ women that will satisfy 95% of the people:
Because of the normal distribution the mean= 0, standard deviation=1.
95 percent means z= +/- 1.96
Max sitting distance for men = 23.5 +(1.96*1.1)= 25.656 inches
Min sitting distance for men = 23.5 -(1.96*1.1)= 21.344 inches
Max sitting distance for women= 22.7 +(1.96*1) = 24.66 inches
Min sitting distance for women = 22.7 -(1.96*1) =