To determine the percentage of values that fall between 7 and 13 in a normal distribution with a mean of 7 and a standard deviation of 2, we can calculate the z-scores for both values and use the standard normal distribution table.
First, we calculate the z-score for 7:
Z1 = (7 - 7) / 2 = 0
Next, we calculate the z-score for 13:
Z2 = (13 - 7) / 2 = 3
Looking up the values in the standard normal distribution table, we find that the area to the left of Z1 (0) is 0.5000, and the area to the left of Z2 (3) is 0.9987.
To find the percentage between 7 and 13, we subtract the area to the left of Z1 from the area to the left of Z2:
Percentage = 0.9987 - 0.5000 = 0.4987
Therefore, approximately 49.87% of the values fall between 7 and 13 in this normal distribution.