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 0.05 ounces.

What percentage of boxes have weights that are more than 1 standard

deviation above the mean? (Use the Empirical Rule 68, 95, 99.7)

a) 15%

b) 14%

c) 20%

d) 16%

d) 16%

Step-by-step explanation:

The empirical rule states that for a normal distribution population with a mean (μ) and standard deviation (σ), the following conditions occur:

68% falls within one standard deviation μ ± σ 95% falls within two standard deviation μ ± 2σ 99.7% falls within three standard deviation μ ± 3σ

Given μ = 16 ounce and σ = 0.05 ounce.

68% falls within one standard deviation = μ ± σ = 16 ± 0.05 = (15.95, 16.05)

the number that falls outside one standard deviation = 100% - 68% = 32%

Therefore percentage of boxes have weights that are more than 1 standard deviation above the mean = 32% / 2 = 16%