Normal Distribution Math Example 2

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Example 2

medium
Heights of adult women are normally distributed with ฮผ=164\mu = 164 cm and ฯƒ=6\sigma = 6 cm. What percentage of women are taller than 176176 cm?

Solution

  1. 1
    Compute how many standard deviations 176176 is from the mean: 176โˆ’1646=2\frac{176 - 164}{6} = 2.
  2. 2
    By the empirical rule, 95%95\% of values lie within 2ฯƒ2\sigma of the mean, so 5%5\% lie outside.
  3. 3
    By symmetry, 5%2=2.5%\frac{5\%}{2} = 2.5\% lie above ฮผ+2ฯƒ\mu + 2\sigma.

Answer

โ‰ˆ2.5%\approx 2.5\%
The normal distribution is symmetric about the mean. Values beyond 22 standard deviations are relatively rare, occurring in only about 5%5\% of cases total (2.5%2.5\% in each tail).

About Normal Distribution

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.

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