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

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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) About Me  (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.