a factory fills bottles of water. the volume of water in the individual bottles is normally distributed with…

a factory fills bottles of water. the volume of water in the individual bottles is normally distributed with a mean of 16.8 ounces and a standard deviation of 0.1 ounces. using the 68 - 95 - 99.7% rule, approximately what percentage of bottles will be filled with more than 17 ounces? enter the answer in the box. %

a factory fills bottles of water. the volume of water in the individual bottles is normally distributed with a mean of 16.8 ounces and a standard deviation of 0.1 ounces. using the 68 - 95 - 99.7% rule, approximately what percentage of bottles will be filled with more than 17 ounces? enter the answer in the box. %

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 17$, $\mu=16.8$ and $\sigma = 0.1$. So $z=\frac{17 - 16.8}{0.1}=\frac{0.2}{0.1}=2$.

Step2: Apply the 68 - 95 - 99.7% rule

The 68 - 95 - 99.7% rule states that about 95% of the data lies within $z=- 2$ and $z = 2$. So the percentage of data outside of $z=-2$ and $z = 2$ is $100%-95% = 5%$. Since the normal distribution is symmetric, the percentage of data with $z>2$ is $\frac{5%}{2}=2.5%$.

Answer:

2.5