Question

Find the percentile corresponding to x=15 if the mean is 12 and the standard deviation is 2.6. a, 13th, b. 82th, c. 89th, d. 88th

Answer 1

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.