A group of 100 students took a math exam, and the scores were normally distributed with a mean of 75 and a standard deviation of 10. What is the percentage of students who scored between 60 and 90 on the exam?

Solution

Since the scores are normally distributed, we can use the z-score formula to standardize the scores and find the percentage of students who scored between 60 and 90. First, we need to find the z-score for a score of 60 and a score of 90. The z-score formula is: z = (x - μ) / σ where x is the score, μ is the mean, and σ is the standard deviation. For x = 60, we have: z = (60 - 75) / 10 = -1.5 For x = 90, we have: z = (90 - 75) / 10 = 1.5 Now we can use a z-score table or a calculator to find the percentage of students who scored between -1.5 and 1.5 standard deviations from the mean. This percentage represents the percentage of students who scored between 60 and 90 on the exam. Using a z-score table, we find that the percentage of students who scored between -1.5 and 1.5 is approximately 86.6%. Therefore, about 86.6% of the students scored between 60 and 90 on the exam.