use the information to answer the question. scores on a video games are normally distributed with a mean…

use the information to answer the question. scores on a video games are normally distributed with a mean score of 190 points and a standard deviation of 15 points. using the 68 - 95 - 99.7% rule, what percentage of players would be expected to score higher than 235 points? enter the answer in the box. %

use the information to answer the question. scores on a video games are normally distributed with a mean score of 190 points and a standard deviation of 15 points. using the 68 - 95 - 99.7% rule, what percentage of players would be expected to score higher than 235 points? enter the answer in the box. %

Answer

Explanation:

Step1: Calculate number of standard - deviations

First, find how many standard - deviations 235 is from the mean. The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 235$, $\mu=190$, and $\sigma = 15$. So, $z=\frac{235 - 190}{15}=\frac{45}{15}=3$.

Step2: Apply the 68 - 95 - 99.7% rule

The 68 - 95 - 99.7% rule states that for a normal distribution, about 99.7% of the data lies within 3 standard - deviations of the mean. That is, $P(\mu - 3\sigma<X<\mu + 3\sigma)=0.997$. The total area under the normal curve is 1. The area outside of $\mu\pm3\sigma$ is $1 - 0.997 = 0.003$. Since the normal distribution is symmetric, the area to the right of $\mu + 3\sigma$ is $\frac{1 - 0.997}{2}$.

Step3: Calculate the percentage

$\frac{1 - 0.997}{2}=0.0015$, and to convert to a percentage, we multiply by 100. So, $0.0015\times100 = 0.15%$.

Answer:

0.15%