QuestionFind the percentile for a score of 156 given a mean of 120 and a standard deviation of 12.

Studdy Solution

STEP 1

Assumptions1. The mean score of the achievement test is120. The standard deviation of the scores is123. A person scored156 on the test4. We are looking for the percentile of the person's score

STEP 2

First, we need to calculate the z-score for the person's score. The z-score is a measure of how many standard deviations an element is from the mean. It is calculated as follows $Z = \frac{X - \mu}{\sigma}$ where- $X$ is the score- $\mu$ is the mean- $\sigma$ is the standard deviation

STEP 3

Now, plug in the given values for the score, the mean, and the standard deviation to calculate the z-score.
$Z = \frac{156 -120}{12}$

STEP 4

Calculate the z-score.
$Z = \frac{156 -120}{12} =3$

STEP 5

Now that we have the z-score, we can use a z-table to find the percentile. A z-table provides the cumulative probability for a standard normal distribution (a distribution with a mean of0 and a standard deviation of1).The percentile is the percentage of scores that fall below a certain score in a distribution. In this case, we want to find the percentage of scores that fall below a z-score of3.
Looking up a z-score of3 in the z-table, we find that the cumulative probability is approximately0.9987. This means that approximately99.87% of scores fall below a z-score of3.
So, the person's score falls at the99.87th percentile, which is closest to the100th percentile among the given options.

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