Question

The weights of boxes of a certain brand of pasta follow an approximately normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounces.

What percentage of boxes have weights that are more than 2 standard deviations below the mean? (Use the Empirical Rule 68, 95, 99.7) ?

Answer 1

2.5%

Explanation:

According to the Empirical Rule:

• 68% of the data in a normal distribution are
  `\pm1\sigma` from the mean
  `\mu`
• 95% of the data in a normal distribution are
  `\pm2\sigma` from the mean
  `\mu`
• 99.7% of the data in a normal distribution are
  `\pm3\sigma` from the mean
  `\mu`

Hence, the percentage of boxes that have weights of more than 2 standard deviations below the mean is
`(100\%-95\%)/(2)=(5\%)/(2)=2.5\%`