use the information to answer the question. a factory fills bottles of water. the volume of water in the…

use the information to answer the question. 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. %

use the information to answer the question. 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 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 68 - 95 - 99.7% rule

The 68 - 95 - 99.7% rule states that about 95% of the data lies within 2 standard deviations of the mean, i.e., $P(\mu - 2\sigma<X<\mu + 2\sigma)\approx0.95$. The total area under the normal - distribution curve is 1. The area outside of $\mu\pm2\sigma$ is $1 - 0.95 = 0.05$. Since the normal distribution is symmetric, the area to the right of $\mu + 2\sigma$ is $\frac{1 - 0.95}{2}$.

Answer:

2.5