a machine at a food - distribution factory fills boxes of rice. the distribution of the weights of filled…

a machine at a food - distribution factory fills boxes of rice. the distribution of the weights of filled boxes of rice has an approximately normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. boxes are often weighed before shipping, and any box with a weight of at most 27.5 ounces is considered underweight and is rejected for distribution. what percentage of filled boxes of rice are rejected for distribution? find the z - table here. 4.0% 24.2% 75.8% 96.0%

a machine at a food - distribution factory fills boxes of rice. the distribution of the weights of filled boxes of rice has an approximately normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. boxes are often weighed before shipping, and any box with a weight of at most 27.5 ounces is considered underweight and is rejected for distribution. what percentage of filled boxes of rice are rejected for distribution? find the z - table here. 4.0% 24.2% 75.8% 96.0%

Answer

Answer:

A. 4.0%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 27.5$ (the value of interest), $\mu=28.2$ (the mean), and $\sigma = 0.4$ (the standard deviation). So, $z=\frac{27.5 - 28.2}{0.4}=\frac{- 0.7}{0.4}=-1.75$.

Step2: Use the z - table

Looking up the z - score of $-1.75$ in the standard normal (z -) table, we find the corresponding cumulative probability. The value in the z - table for $z=-1.75$ is approximately $0.0401\approx4.0%$. This represents the percentage of filled boxes of rice with a weight of at most 27.5 ounces.