Question

question 9 (multiple choice worth 1 points) (lc) the average grade on a test is 82.5%. the grades on the test have a variance of 4%. what is the range of grades on the test? 77.5% to 86.5% 78.5% to 86.5% 78.5% to 82.5% 77.5% to 82.5%

Explanation:

Step1: Find the standard deviation

Variance is given as \(4\%\), and standard deviation (\(\sigma\)) is the square root of variance. So, \(\sigma = \sqrt{4\%} = 2\%\).

Step2: Determine the range of grades

Assuming a normal distribution (or a common range around the mean using standard deviation), the range is typically mean \(\pm\) 2 standard deviations (for a 95% confidence interval - a common range). The mean is \(82.5\%\).
Lower bound: \(82.5\% - 2\times2\% = 82.5\% - 4\% = 78.5\%\)
Upper bound: \(82.5\% + 2\times2\% = 82.5\% + 4\% = 86.5\%\)

Answer:

78.5% to 86.5%