Practice Distribution (Intuition) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A distribution describes how data values are spread out across their range — which values occur, how often, and whether the data is symmetric or skewed.
If you took many measurements, where would most values fall? What's the shape?
Example 1
easyDescribe the distribution of heights of adult men (approximately normally distributed with mean 70 inches and SD 3 inches). What percentage of men are between 64 and 76 inches tall?
Example 2
mediumCompare three distributions: (A) uniform (equal probability for all outcomes), (B) right-skewed (most values small, few very large), (C) bimodal (two peaks). Give a real-world example of each.
Example 3
easyA distribution has mean 50 and median 65. Is this distribution symmetric, left-skewed, or right-skewed? Explain.
Example 4
hardThe Central Limit Theorem says that sample means follow a normal distribution for large n, regardless of the original population's shape. Explain why this is remarkable and give an example using a right-skewed population.