select the correct answer.\nyou have a list of 600 random, normally distributed numbers with a mean of 10…

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean ($\mu\pm\sigma$), about 95% lies within 2 standard deviations of the mean ($\mu\pm2\sigma$), and about 99.7% lies within 3 standard deviations of the mean ($\mu\pm3\sigma$). Here, $\mu = 10$ and $\sigma=2$.

Step2: Analyze option A

The values 8 and 12 are $\mu - \sigma$ and $\mu+\sigma$ respectively. The proportion of data between $\mu - \sigma$ and $\mu+\sigma$ is about 68%. The number of data points is $n = 600$. So the number of data points between 8 and 12 is $0.68\times600=408$.

Step3: Analyze option B

The values 6 and 10 are $\mu - 2\sigma$ and $\mu$ respectively. The proportion of data between $\mu - 2\sigma$ and $\mu$ is $\frac{95%}{2}=47.5%$. The number of data points is $0.475\times600 = 285$.

Step4: Analyze option C

The values 10 and 14 are $\mu$ and $\mu + 2\sigma$ respectively. The proportion of data between $\mu$ and $\mu + 2\sigma$ is $\frac{95%}{2}=47.5%$. The number of data points is $0.475\times600=285$.

Step5: Analyze option D and E

The empirical - rule gives approximate proportions, so we cannot say "exactly" for the number of data points in an interval for a normal distribution.

Answer:

C. About 285 numbers would lie between the values 10 and 14.