scores on a video games are normally distributed with a mean score of 190 points and a standard deviation of…

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. %

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 about 99.7% of the data lies within 3 standard deviations of the mean. That means the percentage of data outside of 3 standard deviations (both above and below) is $100%-99.7% = 0.3%$. Since the normal distribution is symmetric, the percentage of data above 3 standard deviations is $\frac{0.3%}{2}=0.15%$.

Answer:

0.15%