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% of the boxes have weights that are more than 2 standard deviations below the mean.

What is empirical rule?

The empirical rule states that for a normal distribution, 95% of the values are within two standard deviations from the mean.

Given mean of 16 ounces and a standard deviation of 0.5 ounces.

Hence:

95% is within 16 ± 2(0.5) = (15, 17)

number above 2 standard deviation = 5%/2 = 2.5%

2.5% of the boxes have weights that are more than 2 standard deviations below the mean.

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