At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Using the empirical rule, what percentage of students at the college have a GPA between 2.3 and 3.5? 84.13% 68% 99.7% 95%

Answer:68%Step-by-step explanation:According to the empirical rule:68% of the data values lie within one standard deviation from the mean i.e. from z = -1 to z = 1 we have 68% of the data values95% of the data values lie within two standard deviations of the mean99.7% of the data values lie within three standard deviations of the meanSo first we have to find how many standard deviations away from the mean are the given two values. This can be done by converting them into z scores.The formula to calculate the z-score is:[tex]z=\frac{\text{Data Value}-\text{Mean}}{\text{Standard Deviation}}[/tex]Using the given values in above formula, we get:For x = 2.3[tex]z = \frac{2.3-2.9}{0.6}=-1[/tex]For x = 3.5[tex]z = \frac{3.5-2.9}{0.6}=1[/tex]This means we have to tell how many data values are within one standard deviation of the mean. According to the empirical rule 68% of the values are between z= -1 and z = 1. So the answer is 68%