Question

a math teachers midterm is worth 200 points. the mean of the test is 143 and the standard deviation is 15.7. if the scores have a bell - shaped distribution, what percentage of the scores are between 111.6 and 174.4? (1 point) about 99.7% about 68% about 62.8% about 95%

Explanation:

Step1: Calculate the number of standard deviations from the mean

For the lower bound \(111.6\): \(\frac{143 - 111.6}{15.7}=\frac{31.4}{15.7} = 2\)
For the upper bound \(174.4\): \(\frac{174.4 - 143}{15.7}=\frac{31.4}{15.7}=2\)

Step2: Apply the empirical rule

The empirical rule for a normal (bell - shaped) distribution states that approximately \(95\%\) of the data lies within \(2\) standard deviations of the mean (\(\mu\pm2\sigma\)).

Answer:

about \(95\%\)