select the correct answer.\nthe scores received by students completing a geology exam are normally…

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $x = 52$, $\mu=122$, and $\sigma = 35$, we have $z=\frac{52 - 122}{35}=\frac{-70}{35}=- 2$. The z - score for the mean $x = 122$ is $z=\frac{122 - 122}{35}=0$.

Step2: Use the empirical rule

The empirical rule for a normal distribution states that about 95% of the data lies within $z=-2$ and $z = 2$, and the distribution is symmetric about the mean. The percentage of data between $z=-2$ and $z = 0$ is half of the percentage of data between $z=-2$ and $z = 2$. Since the percentage of data between $z=-2$ and $z = 2$ is 95%, the percentage of data between $z=-2$ and $z = 0$ is $\frac{95%}{2}=47.5%$.

Answer:

D. 47.5%