High School

Suppose SAT Writing scores are normally distributed with a mean of 497 and a standard deviation of 114. A university plans to admit students whose scores are in the top 30%.

What is the minimum score required for admission? Round your answer to the nearest whole number.

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