Question

Mathematics achievement scores from a group of tenth graders show a normal distribution with a mean of 70 and a standard deviation of 10. Approximately what percentage of students scored between 50 and 80?

Answer 1

To find the percentage of students who scored between 50 and 80 in a normal distribution with a mean of 70 and a standard deviation of 10, you can calculate the z-scores for these values and look up the corresponding percentages. The percentage of students who scored between 50 and 80 is approximately 82%.

Step-by-step explanation:

To find the percentage of students who scored between 50 and 80, we need to calculate the z-scores for these values using the formula:

z = (x - mean) / standard deviation

For an x value of 50:

z = (50 - 70) / 10 = -2

For an x value of 80:

z = (80 - 70) / 10 = 1

The z-score of -2 corresponds to approximately 2.28% and the z-score of 1 corresponds to approximately 84.13%. Therefore, the percentage of students who scored between 50 and 80 is approximately 84.13% - 2.28% = 81.85%, or approximately 82%.