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Answer :
Final answer:
The minimum SAT Writing score required for admission is 562.
Explanation:
To find the minimum score required for admission, we need to find the SAT Writing score that corresponds to the top 30% of the distribution. The top 30% corresponds to an area under the curve of 0.3. Using the mean and standard deviation provided, we can use a standard normal distribution table or a calculator to find the z-score associated with the top 30%. From the z-score, we can then calculate the corresponding SAT Writing score.
Using a standard normal distribution table, the z-score associated with the top 30% is approximately 0.524. We can then use the formula z = (x - mean) / standard deviation to find the corresponding SAT Writing score:
0.524 = (x - 497) / 114
Solving for x, we get:
x = 0.524 * 114 + 497
x ≈ 561.536
Rounded to the nearest whole number, the minimum score required for admission is 562.
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Answer:
The minimum score required for admission to the nearest whole number = 557
Step-by-step explanation:
We solve this using z score formula.
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Top 30% of the candidates is a ranking that is equivalent to = 100 - 30% = 70th percentile.
The z score of 70th percentile = 0.524
Mean = 497
Standard deviation of 114.
Minimum score = raw score = ???
Hence:
0.524 = x - 497/114
Cross Multiply
0.524 × 114 = x - 497
59.736 = x - 497
x = 59.736 + 497
x = 556.736
The minimum score required for admission to the nearest whole number = 557
