Final answer:
Approximately 34.13% of the data falls between 23 and 25 in a normally distributed data set with a mean of 25 and a standard deviation of 2.
Step-by-step explanation:
The percentage of data that falls between 23 and 25 in a normally distributed data set with a mean of 25 and a standard deviation of 2 can be found by calculating the area under the normal distribution curve between those two values.
First, we need to standardize the values using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For 23, Z = (23 - 25) / 2 = -1.
Next, for 25, Z = (25 - 25) / 2 = 0.
The area between these two Z values can be found using a standard normal distribution table or a calculator.
If we use a standard normal distribution table, we can find that the area to the left of Z = -1 is 0.1587 and the area to the left of Z = 0 is 0.5. To find the area between these two Z values, we subtract the area of Z = -1 from the area of Z = 0: 0.5 - 0.1587 = 0.3413. This means that approximately 34.13% of the data falls between 23 and 25 in the given normally distributed data set.