Practice Normal Distribution in Statistics

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

Quick Recap

A symmetric, bell-shaped probability distribution where most data clusters around the mean, with probabilities decreasing symmetrically toward the tails.

Heights, test scores, measurement errors - many real phenomena cluster around an average with decreasing frequency toward extremes. The bell curve captures this pattern: most values are 'average,' few are extreme.

Example 1

medium
IQ scores follow a normal distribution with mean \mu = 100 and standard deviation \sigma = 15. Using the 68-95-99.7 rule, what percentage of people have IQs between 85 and 115?

Example 2

hard
Birth weights are normally distributed with \mu = 3.5 kg and \sigma = 0.5 kg. What percentage of babies weigh between 2.5 and 4.5 kg?

Example 3

medium
A factory produces bolts with mean length 10 cm and standard deviation 0.2 cm (normally distributed). What percentage of bolts are longer than 10.4 cm?

Example 4

medium
A normal distribution has mean \mu = 50 and standard deviation \sigma = 4. Using the 68-95-99.7 rule, what percentage of values lie between 42 and 58?
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