In a distribution of scores with a mean of 234 and a standard deviation of 47, what is in the 43rd percentile ? and what formula do i use ?
To find the value at the 43rd percentile in a distribution with a mean and standard deviation, you can use the z-score formula. The z-score formula allows you to convert any given value from a normal distribution into a standardized score, which represents the number of standard deviations it is away from the mean.
The formula for calculating the z-score is:
z = (X - μ) / σ
where:
- X is the value for which you want to find the percentile,
- μ is the mean of the distribution, and
- σ is the standard deviation of the distribution.
To find the value at the 43rd percentile, you need to determine the corresponding z-score first. You can use a z-table or a statistical calculator to find the z-score that corresponds to the 43rd percentile. The z-score will give you the number of standard deviations from the mean at which the value lies.
Once you have the z-score, you can rearrange the formula to solve for X:
X = (z * σ) + μ
In this case, the mean (μ) is 234 and the standard deviation (σ) is 47. We need to find the value at the 43rd percentile. Now, let's calculate the z-score:
To find the z-score for the 43rd percentile, subtract 0.43 from 1 (since the z-table provides the cumulative probabilities from the left tail), giving you a z-score of 0.57.
Now, plug the values into the formula:
X = (0.57 * 47) + 234
Calculate the result:
X ≈ 264.79
Therefore, at the 43rd percentile, the value in the distribution is approximately 264.79.