use the information to answer the question.\na data set is normally distributed. the mean of the data is…
use the information to answer the question.\na data set is normally distributed. the mean of the data is 9.2, and the standard deviation is 1.8.\nusing the 68 - 95 - 99.7 rule, what percentage of the data points are greater than 11? enter the answer in the box.\n%
Answer
Explanation:
Step1: Calculate the z - score
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 11$, $\mu=9.2$, and $\sigma = 1.8$. So $z=\frac{11 - 9.2}{1.8}=\frac{1.8}{1.8}=1$.
Step2: Recall the 68 - 95 - 99.7 rule
The 68 - 95 - 99.7 rule states that for a normal distribution, about 68% of the data lies within 1 standard deviation of the mean ($\mu\pm\sigma$), 95% within 2 standard deviations ($\mu\pm2\sigma$), and 99.7% within 3 standard deviations ($\mu\pm3\sigma$). The percentage of data within 1 standard deviation of the mean is 68%. So the percentage of data outside of $\mu\pm1\sigma$ is $100 - 68=32%$. Since the normal distribution is symmetric, the percentage of data greater than $\mu + \sigma$ is $\frac{32}{2}=16%$.
Answer:
16