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Answer :
Final Answer
In the group of good readers and good spellers, the percentage of participants who correctly read at least 92 words is approximately 32.34%.
Explanation
To calculate the percentage of participants who correctly read at least 92 words in the good readers and good spellers group, we need to use the z-score formula and then find the corresponding percentage from the standard normal distribution table.
First, we calculate the z-score:
z = (X - μ) / σ
Where:
X = 92 (the value we want to find the percentage for)
μ = 90.2 (mean)
σ = 3 (standard deviation)
z = (92 - 90.2) / 3 ≈ 0.6
Next, we find the percentage from the standard normal distribution table for z = 0.6. From the table, we find that the percentage is approximately 0.7257.
However, we are interested in the percentage of participants who scored at least 92 words, which is the area to the right of the z-score. Since the total area under the normal distribution curve is 1, we subtract the calculated percentage from 1 to get the percentage of participants who scored at least 92 words:
Percentage = 1 - 0.7257 ≈ 0.2743
Convert the percentage to a percentage value by multiplying by 100:
Percentage ≈ 0.2743 * 100 ≈ 27.43%
So, approximately 27.43% of participants in the good readers and good spellers group scored at least 92 words.
Learn more about corresponding percentage.
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