The 20 tallest buildings in the world have an average height of 1,667.25 feet, with a standard deviation of 318.31 feet. The Zifeng Tower and the Wuhan Center have heights of 1,476 feet and 1,437 feet, respectively. The Shanghai Tower and Marina 101 have z-scores of 1.27 and - 0.84, respectively.

Part A: List these four buildings in order from shortest to tallest.

Part B: Mathematically explain your reasoning and be sure to include all necessary calculations.

Marina, Wuhan center, Zifeng Tower, Shangai Tower

Step-by-step explanation:

Using the z-scores of the Shangai tower and the Marina, we can calculate their heights

Mathematically, the z-score or standard score can be calculated as follows

Zscore = X - μ/σ

where σ and μ represents the standard deviation and the population mean respectively.

For Shaghai Tower;

1.27 = (X - 1667.25) / 318.31

318.31 * 1.27 = X - 1667.25

404.25 = X - 1667.25

X = 1667.25 + 404.25 = 2071.50

The height of the Shaghai Tower is 2071.50 feet

For Marina, we use the same procedure;

-0.84 = (X - 1667.25) / 318.31

318.31 * - 0.84 = X - 1667.25

-267.38 = X - 1667.25

X = 1667.25 - 267.38 = 1399.87

The height of Marina building is 1399.87

Listing the buildings' height in ascending order we have; Marina, Wuhan center, Zifeng Tower, Shangai Tower

The reasoning behind this can be mathematically explained in terms of the z-score. The standard score of the heights of the building give us an insight as to how tall the buildings can be.

Since they are in the same population i. e building heights, the higher the z-score, the higher the height of the building. A positive z-score indicates a height taller than the average while a negative z-score indicate a height lower than the average height which is the mean