Answered

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 :

Answer:

2.5%

Step-by-step explanation:

According to the Empirical Rule:

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

Hence, the percentage of boxes that have weights of more than 2 standard deviations below the mean is [tex]\frac{100\%-95\%}{2}=\frac{5\%}{2}=2.5\%[/tex]

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