a data set is normally distributed. the mean of the data is 9.2, and the standard deviation is 1.8. using…
a data set is normally distributed. the mean of the data is 9.2, and the standard deviation is 1.8. using 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: Apply the 68 - 95 - 99.7 rule
The 68 - 95 - 99.7 rule states that about 68% of the data lies within 1 standard deviation of the mean, i.e., between $\mu-\sigma$ and $\mu+\sigma$. So the percentage of data within $z=- 1$ and $z = 1$ is 68%. The percentage of data outside of this range is $100 - 68=32%$. Since the normal distribution is symmetric, the percentage of data with $z>1$ is $\frac{32}{2}=16%$.
Answer:
16