Final answer:
The scores that are within one standard deviation of the mean are 80 to 90.
Step-by-step explanation:
In this problem, the test scores are normally distributed with a mean of 85 and a standard deviation of 5. To find the scores that are within one standard deviation of the mean, we need to find the range from the mean minus the standard deviation to the mean plus the standard deviation.
Using the formula, we have:
Mean - Standard Deviation = 85 - 5 = 80
Mean + Standard Deviation = 85 + 5 = 90
Therefore, the scores that are within one standard deviation of the mean are 80 to 90.