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

use the information to answer the question.\na 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.\nusing 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.\n%

use the information to answer the question.\na 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.\nusing 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.\n%

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 the 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 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 $\frac{1 - 0.95}{2}=0.025$.

Answer:

2.5