Final answer:
To find the percentage of students who scored between 75 and 80 on the test, we need to find the area under the normal distribution curve between those two scores. Using the formula for z-scores, we can standardize the scores and then use a standard normal distribution table or calculator to find the probabilities.
Step-by-step explanation:
To find the percentage of students who scored between 75 and 80 on the test, we need to find the area under the normal distribution curve between those two scores. First, we need to standardize the scores by finding the z-scores using the formula: z = (x - mean) / standard deviation. For the score 75: z1 = (75 - 75) / 15 = 0, and for the score 80: z2 = (80 - 75) / 15 = 0.33. Using a standard normal distribution table or calculator, we can find the corresponding probabilities for z1 and z2. Subtracting the probability corresponding to z1 from the probability corresponding to z2 gives us the percentage of students who scored between 75 and 80.
Using the standard normal distribution table, we find that the probability corresponding to z = 0 is 0.5, and the probability corresponding to z = 0.33 is 0.6293. Therefore, the percentage of students who scored between 75 and 80 is 0.6293 - 0.5 = 0.1293 or 12.93%.