Normal Distribution Statistics Example 4

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Example 4

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

Solution

  1. 1
    Step 1: The interval 42 to 58 is 50±850 \pm 8, which is μ±2σ\mu \pm 2\sigma because 8=2(4)8 = 2(4).
  2. 2
    Step 2: By the 68-95-99.7 rule, about 95% of values lie within two standard deviations of the mean.

Answer

Approximately 95%95\% of the values lie between 42 and 58.
The empirical rule gives quick approximations for normal data. Recognising intervals in terms of standard deviations lets us answer probability questions without a calculator.

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 →

More Normal Distribution Examples

Example 1 medium

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Example 2 hard

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Example 3 medium

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

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