Question

at a local high school, gpas are normally distributed with a mean of 2.9 and standard deviation of 0.6. what percentage of students at the high school have a gpa between 2.3 and 3.5? 84% 68% 95% 99.7%

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value.
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: Use the empirical rule

The empirical rule for a normal distribution states that approximately 68% of the data lies within 1 standard deviation of the mean. That is, the percentage of data between $z=-1$ and $z = 1$ is 68%.

Answer:

68%