Question

at one college, gpas 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? (1 point) 95% 84.13% 99.7% 68%

Explanation:

Step1: Calculate the number of standard deviations from the mean

For \(x = 2.3\): \(z_1=\frac{2.3 - 2.9}{0.6}=\frac{- 0.6}{0.6}=-1\)
For \(x = 3.5\): \(z_2=\frac{3.5 - 2.9}{0.6}=\frac{0.6}{0.6}=1\)

Step2: Apply the empirical rule

The empirical rule states that for a normal distribution, approximately \(68\%\) of the data lies within \(z=-1\) and \(z = 1\) (i.e., \(\mu\pm\sigma\)), approximately \(95\%\) lies within \(z=-2\) and \(z = 2\) (\(\mu\pm2\sigma\)), and approximately \(99.7\%\) lies within \(z=-3\) and \(z = 3\) (\(\mu\pm3\sigma\))

Answer:

68%