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Answer :
Final answer:
Dwayne's percentile score is found by calculating his z-score, which is the number of standard deviations his test score is from the mean, and then finding the corresponding percentile from the standard normal distribution. Dwayne's score of 87 corresponds to the 97.5th percentile, making the answer Option A: 97.5 percentile.
Explanation:
To find Dwayne's percentile score, we need to calculate how many standard deviations his score is from the mean, known as the z-score, and then use the standard normal distribution to find the corresponding percentile.
The formula for the z-score is:
Z = (X - μ) / σ
where X is the score, μ is the mean, and σ is the standard deviation.
Given Dwayne's score (87), the mean (78), and standard deviation (4.5), the z-score calculation is:
Z = (87 - 78) / 4.5 ≈ 2
Using a standard normal distribution table or a calculator with the invNorm function, you can find the percentile that corresponds to a z-score of 2.
The percentile score that matches a z-score of 2 is typically around the 97.5th percentile.
Therefore, Dwayne's percentile score would be Option A: 97.5 percentile.
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Rewritten by : Barada
The percentile score would most likely be 97.5, Hope this helps!! :D
