Normal Distribution Math Example 3

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

Example 3

hard
A machine fills bottles with a mean of 500500 mL and standard deviation 44 mL (normally distributed). What percentage of bottles contain between 492492 mL and 508508 mL?

Solution

  1. 1
    492=500โˆ’2(4)=ฮผโˆ’2ฯƒ492 = 500 - 2(4) = \mu - 2\sigma and 508=500+2(4)=ฮผ+2ฯƒ508 = 500 + 2(4) = \mu + 2\sigma.
  2. 2
    By the empirical rule, approximately 95%95\% of bottles fall within 22 standard deviations.

Answer

โ‰ˆ95%\approx 95\%
Recognizing the bounds as ฮผยฑ2ฯƒ\mu \pm 2\sigma allows direct application of the empirical rule without needing z-tables.

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.

Learn more about Normal Distribution โ†’

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