Practice Normal Distribution in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The normal distribution (also called the Gaussian distribution or bell curve) is a continuous probability distribution that is symmetric about its mean, with data tapering off equally on both sides following a precise mathematical rule.

The normal distribution describes data that clusters symmetrically around the mean with a characteristic bell shape — most values are near the mean, and extreme values become rapidly less likely.

Example 1

medium
Scores on a test are normally distributed with mean \mu = 75 and standard deviation \sigma = 10. What percentage of students scored between 65 and 85?

Example 2

medium
Heights of adult women are normally distributed with \mu = 164 cm and \sigma = 6 cm. What percentage of women are taller than 176 cm?

Example 3

hard
A machine fills bottles with a mean of 500 mL and standard deviation 4 mL (normally distributed). What percentage of bottles contain between 492 mL and 508 mL?

Example 4

medium
A standardized exam has scores that are approximately normal with mean 500 and standard deviation 100. About what percent of students score between 400 and 700?
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