Final answer:
To determine the percentile for x=15 with a mean of 12 and a standard deviation of 2.6, the z-score is calculated to be approximately 1.15. This z-score corresponds to the 88th percentile, thus the answer is d. 88th.
Step-by-step explanation:
To find the percentile corresponding to x=15 given a mean of 12 and a standard deviation of 2.6, we need to calculate the z-score and then determine the percentile that corresponds with that z-score in the normal distribution.
First, calculate the z-score using the formula:
Z = (X - μ) / σ
Where X is the score in question, μ (mu) is the mean, and σ (sigma) is the standard deviation.
Inserting our values we get:
Z = (15 - 12) / 2.6
Z = 3 / 2.6
Z ≈ 1.15
Using a standard normal distribution table or a calculator, we find that the z-score of 1.15 roughly corresponds to the 88th percentile.
Therefore, the answer is d. 88th.