a large set of test scores is normally distributed with a mean score of 187. 68% of test - takers had scores…
a large set of test scores is normally distributed with a mean score of 187. 68% of test - takers had scores between 171 and 203. what is the standard deviation for the data? use the empirical rule.\n$sigma=square$ points
Answer
Explanation:
Step1: Recall the Empirical Rule
The Empirical Rule states that for a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean, i.e., $\mu-\sigma$ and $\mu + \sigma$.
Step2: Set up equations
Let the mean $\mu = 187$. We know that the lower - bound is $\mu-\sigma=171$ and the upper - bound is $\mu+\sigma = 203$. We can use either equation to find $\sigma$. Using $\mu-\sigma=171$, we can rewrite it as $\sigma=\mu - 171$.
Step3: Calculate the standard deviation
Substitute $\mu = 187$ into the equation $\sigma=\mu - 171$. So, $\sigma=187 - 171=16$.
Answer:
16