The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?

Accepted Solution

Answer:95% of students are between 14 and 18 years oldStep-by-step explanation:First we calculate the Z-scoresWe 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