Normal Distribution Statistics Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

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

Solution

  1. 1
    Step 1: 85 is one standard deviation below the mean: 100โˆ’15=85100 - 15 = 85.
  2. 2
    Step 2: 115 is one standard deviation above the mean: 100+15=115100 + 15 = 115.
  3. 3
    Step 3: By the 68-95-99.7 rule, approximately 68% of data falls within one standard deviation of the mean.

Answer

Approximately 68%.
The empirical rule (68-95-99.7) gives quick estimates for normal distributions: about 68% within 1ฯƒ, 95% within 2ฯƒ, and 99.7% within 3ฯƒ of the mean.

About Normal Distribution

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.

Learn more about Normal Distribution โ†’

More Normal Distribution Examples

Example 2 hard

Birth weights are normally distributed with [formula] kg and [formula] kg. What percentage of babies

Example 3 medium

A factory produces bolts with mean length 10 cm and standard deviation 0.2 cm (normally distributed)

Example 4 medium

A normal distribution has mean [formula] and standard deviation [formula]. Using the 68-95-99.7 rule

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