Question

match the frequency distribution of 150 rolls of a dodecahedron (a 12 - sided die) with one of the histograms shown below. which histogram shows a distribution that would likely result from 150 rolls of a dodecahedron? (options: a, b, c, d with corresponding histograms as shown in the image)

Explanation:

Step1: Understand Dodecahedron Rolls

A fair dodecahedron (12 - sided die) has each face (number 1 - 12) equally likely. When rolled many times (150 rolls), the frequency distribution should be approximately uniform (each number has roughly the same frequency), or show small random variations around a uniform distribution.

Step2: Analyze Histograms

• Histogram A: Shows a decreasing trend (frequencies get smaller as the number on the die increases), which is not consistent with a fair dodecahedron.
• Histogram B: Shows an increasing trend (frequencies get larger as the number on the die increases), which is not consistent with a fair dodecahedron.
• Histogram C: The bars have relatively similar heights (with small variations), which is consistent with the expected uniform (or nearly uniform) distribution from rolling a fair dodecahedron many times.
• Histogram D: Shows a bell - shaped (normal - like) distribution, which is not expected for a discrete uniform distribution of a die roll.

Answer:

C. (The histogram with relatively uniform bar heights, showing small random variations around a uniform distribution, consistent with 150 rolls of a fair dodecahedron)