The scores achieved by students in America make the news often, and all kinds of conclusions are drawn based on these scores. The ACT Assessment is designed to assess high school students’ general educational development and their ability to complete college-level work. One of the categories tested is Science Reasoning. The mean ACT test score for all high school graduates in 2008 in Science Reasoning was 20.8 with a standard deviation of 4.6.
a. According to Chebyshev’s theorem, at least what percent of high school graduates’ACT scores in Science Reasoning were between 11.6 and 30.0?
b. If we know that ACT scores are normally distributed, what percent of ACT Science Reasoning scores were between 11.6 and 30.0?