3.2 A certain standardized test's math scores have a bell-shaped distribution with a mean of 525 and a standard deviation of 114 . Complete parts (a) through (c). (a) What percentage of standardized test scores is between 183 and 867 ? Part 1 of 3.2 (Round to one decimal place as needed.)

To find the percentage of standardized test scores between 183 and 867, we can use the properties of the bell-shaped (normal) distribution. First, we convert the raw scores into z-scores using the formula z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. For the lower bound (183): z1 = (183 - 525) / 114 ≈ -3.00 For the upper bound (867): z2 = (867 - 525) / 114 ≈ 3.00 Using the z-table or a calculator, we can find the percentage of data that corresponds to these z-scores. The area under the normal curve between z = -3 and z = 3 is approximately 99.7%. Therefore, about 99.7% of the standardized test scores fall between 183 and 867. To summarize, the answer to part (a) is approximately: 99.7%