Practice Normal Distribution in Math

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

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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.

Showing a random 20 of 50 problems.

Example 1

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IQ scores are normal with mean 100100, SD 1515. What percent of people have IQ above 130130?

Example 2

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Test scores are normal with mean 500500, SD 100100. What percent score below 400400?

Example 3

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Cholesterol levels in adults are approximately normal with μ=200\mu = 200 mg/dL and σ=25\sigma = 25 mg/dL. What percent of adults have cholesterol between 150150 and 250250 mg/dL?

Example 4

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Weights are normal, mean 6060 kg, SD 88 kg. Between what two weights do about 95% fall?

Example 5

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A normal distribution has μ=12\mu = 12 and σ=2\sigma = 2. What value sits at the 8484th percentile?

Example 6

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For a standard normal distribution, what is the value of μ+σ\mu+\sigma?

Example 7

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Scores are normal with mean 100100, SD 1515. Between which values do about 68% of scores fall?

Example 8

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For the standard normal distribution, what are the mean and standard deviation?

Example 9

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Birth weights are normal with mean 3.43.4 kg and SD 0.50.5 kg. Between what two weights do about 99.7%99.7\% of babies fall?

Example 10

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A normal distribution has μ=100\mu = 100 and σ=12\sigma = 12. Using the empirical rule, estimate P(76<X<112)P(76 < X < 112).

Example 11

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Heights are normal with mean 170170 cm. What percent of people are taller than 170170 cm?

Example 12

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True or false: a normal distribution's mean, median, and mode are all equal.

Example 13

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Explain why incomes are typically NOT modeled as normal, and give one alternative distribution often used.

Example 14

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IQ is normal with μ=100\mu=100, σ=15\sigma=15. What fraction of people have IQ between 8585 and 130130?

Example 15

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XX is normal with μ=25\mu = 25, σ=4\sigma = 4. Find the value cc such that P(X<c)=0.025P(X < c) = 0.025.

Example 16

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In a normal distribution, what percent of data lies between −1-1 and +2+2 standard deviations from the mean?

Example 17

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Adult male heights are normal: μ=70\mu = 70 in, σ=3\sigma = 3 in. In a sample of 10001000 men, about how many are taller than 7676 inches?

Example 18

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Heights are normal with mean 170170 cm, SD 1010 cm. What percent are between 160160 and 180180 cm?

Example 19

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SAT scores are normal with μ=1050\mu = 1050 and σ=200\sigma = 200. What percent score between 850850 and 14501450?

Example 20

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For two independent normal random variables X∼N(μ1,σ12)X \sim N(\mu_1, \sigma_1^2) and Y∼N(μ2,σ22)Y \sim N(\mu_2, \sigma_2^2), what is the distribution of X+YX + Y?
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