Normal Distribution Statistics Example 3

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

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?

Solution

  1. 1
    Step 1: 10.4=10+2(0.2)10.4 = 10 + 2(0.2), so 10.4 cm is 2ฯƒ above the mean. By the empirical rule, 95% falls within ยฑ2ฯƒ.
  2. 2
    Step 2: 5% is outside ยฑ2ฯƒ, split equally: 2.5% above and 2.5% below. So about 2.5% are longer than 10.4 cm.

Answer

Approximately 2.5%.
Using the symmetry of the normal distribution and the empirical rule, we can find tail probabilities by halving the percentage outside the given range.

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†’

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