use the information to answer the question. a data set is normally distributed. the mean of the data is 9.2…
use the information to answer the question. 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. %
Answer
Explanation:
Step1: Calculate 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, which means 32% of the data lies outside 1 standard deviation of the mean. Since the normal distribution is symmetric, 16% of the data is greater than 1 standard deviation above the mean.
Answer:
16