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. what percentage of filled boxes of rice have a weight less than 27.9 ounces? find the z - table here. 22.7% 38.2% 61.8% 77.3%

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. what percentage of filled boxes of rice have a weight less than 27.9 ounces? find the z - table here. 22.7% 38.2% 61.8% 77.3%

Answer

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 27.9$, $\mu=28.2$, and $\sigma = 0.4$. $z=\frac{27.9 - 28.2}{0.4}=\frac{- 0.3}{0.4}=-0.75$

Step2: Find the percentage from the z - table

Looking up the z - score of $-0.75$ in the standard normal (z -) table, the value corresponding to $z=-0.75$ is $0.2266\approx22.7%$

Answer:

22.7%