Question

value: 3 mr. emmer gave a test in his chemistry class. the scores were normally distributed with a mean of 82 and a standard deviation of 4. what percent of students would you expect to score between 78 and 86? (remember to refer to the normal distribution located on page 8 of the lesson) a. 47.5% b. 68% c. 34% d. 13.5%

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 data - point.
For $x = 78$, $z_1=\frac{78 - 82}{4}=\frac{-4}{4}=-1$.
For $x = 86$, $z_2=\frac{86 - 82}{4}=\frac{4}{4}=1$.

Step2: Use the empirical rule of normal distribution

The empirical rule (68 - 95 - 99.7 rule) states that for a normal distribution, approximately 68% of the data lies within 1 standard deviation of the mean, i.e., between $z=-1$ and $z = 1$.

Answer:

B. 68%