The normal distribution (bell curve) is a symmetric, bell-shaped probability distribution where most data clusters around the mean, with probabilities decreasing symmetrically toward the tails. It is defined by two parameters: the mean and the standard deviation.
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.
Showing a random 20 of 50 problems.
Example 1
easy
A normal distribution has mean 100. The value 100 is at what percentile?The mean (100) is at the 50th percentile
Example 2
medium
Test scores are normal with μ=500, σ=100. Roughly what percent score above 600?What percent score above 600? (600 = μ + σ)
Example 3
medium
A normal distribution has μ=50, σ=5. About 95% of data lies between which values?About 95% of data lies between 40 and 60 (μ ± 2σ)
Example 4
medium
For μ=100, σ=15, find the z-score of x=130.
Example 5
easy
Adult IQ scores are designed with μ=100, σ=15. About what percent lies between 85 and 115?
Example 6
easy
Are the tails of a normal distribution ever exactly reaching zero?
Example 7
hard
What is the median of a normal distribution with μ=25, σ=4?
Example 8
medium
In a normal distribution, what fraction of data lies between z=−1 and z=2?
Example 9
hard
Two normal curves have the same mean but σA=2,σB=5. Which is taller at the center?
Example 10
medium
For a normal distribution, about what percent of data lies BELOW the mean minus 1 SD?
Example 11
easy
What is the value of the standard normal distribution's mean and SD?
Example 12
medium
A z-score of 0 corresponds to a value equal to what?
Example 13
hard
A normal distribution has μ=0,σ=2. Find P(∣X∣>4).
Example 14
easy
Approximately what percent of data lies within ONE standard deviation of the mean in a normal distribution?About 68% of data lies within one standard deviation of the mean
Example 15
medium
SAT scores have μ=1000, σ=200. A score of 1400 is at what percentile, roughly?
Example 16
medium
IQ scores follow a normal distribution with mean μ=100 and standard deviation σ=15. Using the 68-95-99.7 rule, what percentage of people have IQs between 85 and 115?
Example 17
medium
For μ=50, σ=4, what value lies 1.5 SDs above the mean?
Example 18
medium
A normal distribution has μ=70, σ=4. What value is 2 standard deviations above the mean?Where is μ + 2σ on this curve?
Example 19
easy
For a normal distribution, the mean, median, and mode are all located where?
Example 20
easy
Which two parameters fully define a normal distribution?