Final answer:
The percent of scores falling between 70 and 80 on a normally distributed test with a mean of 60 and a standard deviation of 15 is approximately 15.96%.
Step-by-step explanation:
To find what percent of scores fall between 70 and 80 on a test with a normal distribution, mean of 60, and standard deviation of 15, we need to calculate the Z-scores for both the lower bound (70) and the upper bound (80) and then use the standard normal distribution table to find the corresponding probabilities.
The formula for the Z-score is:
Z = (X - μ) / σ
Where X is the score, μ is the mean, and σ is the standard deviation.
For the lower bound (70):
Z = (70 - 60) / 15 = 10 / 15 ≈ 0.67
For the upper bound (80):
Z = (80 - 60) / 15 = 20 / 15 ≈ 1.33
We then use a Z-table or calculator to find the percent of scores falling between these two Z-scores. The area under the curve between these two values represents the percentage of scores that fall between 70 and 80.
For Z = 0.67, the table gives us the area to the left, which is approximately 0.7486. For Z = 1.33, the area to the left is approximately 0.9082.
To find the percentage between the two Z-scores, we subtract the lower Z-score's area from the higher Z-score's area:
Percentage = 0.9082 - 0.7486 = 0.1596
Therefore, approximately 15.96% of the scores fall between 70 and 80.