Answer:mean = 50
standard deviation = 10 (example answer)
Explanation:
To find the 90th percentile using the mean and standard deviation, you can use the concept of the standard score (also known as the z-score). The z-score measures the number of standard deviations an individual data point is from the mean.
Here are the steps to find the 90th percentile:
Determine the z-score corresponding to the desired percentile. In this case, since you want the 90th percentile, the z-score will correspond to that percentile. You can find the z-score using a standard normal distribution table or a statistical calculator. For the 90th percentile, the z-score is approximately 1.28.
Use the formula for the z-score: z = (x - mean) / standard deviation. Rearrange the formula to solve for the desired value, x: x = (z * standard deviation) + mean.
Substitute the z-score and the given mean and standard deviation into the formula to find the value at the 90th percentile.
For example, let's say the mean is 50 and the standard deviation is 10. To find the value at the 90th percentile:
z = 1.28 (z-score for the 90th percentile)
mean = 50
standard deviation = 10
x = (1.28 * 10) + 50
x = 12.8 + 50
x = 62.8
Therefore, the value at the 90th percentile, given the mean of 50 and standard deviation of 10, is approximately 62.8.