Answer:
95% of students are between 14 and 18 years old
Step-by-step explanation:
First we calculate the Z-scores
We know the mean and the standard deviation.
The mean is:
[tex]\mu=16[/tex]
The standard deviation is:
[tex]\sigma=1[/tex]
The z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=14 the Z-score is:
[tex]Z_{14}=\frac{14-16}{1}=-2[/tex]
For x=18 the Z-score is:
[tex]Z_{18}=\frac{18-16}{1}=2[/tex]
Then we look for the percentage of the data that is between [tex]-2 <Z <2[/tex] deviations from the mean.
According to the empirical rule 95% of the data is less than 2 standard deviations of the mean. This means that 95% of students are between 14 and 18 years old
