SOLUTION: To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based o

Question 1192261: To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based on the scores on a reading achievement exam. The average score is found to be 122.6 with a standard deviation of 18. Assume that the variable is normally distributed.What is the 75th percentile score? Write your answer to the nearest whole number.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to find the 75th percentile score:
**1. Understand Percentiles and Z-scores**
* The 75th percentile is the score below which 75% of the data falls.
* Z-scores measure how many standard deviations a particular score is away from the mean.
**2. Find the Z-score for the 75th Percentile**
You can use a Z-table or a calculator with statistical functions to find the Z-score corresponding to the 75th percentile (0.75). The Z-score is approximately 0.67.
**3. Use the Z-score Formula**
The formula to convert a Z-score to a raw score (the actual test score) is:
X = μ + (Z * σ)
Where:
* X is the raw score you're trying to find
* μ is the mean of the distribution (122.6)
* σ is the standard deviation (18)
* Z is the Z-score (0.67)
**4. Calculate**
X = 122.6 + (0.67 * 18)
X = 122.6 + 12.06
X = 134.66
**5. Round**
Rounding to the nearest whole number, the 75th percentile score is 135.

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