Suppose SAT Writing score are normally distributed 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.

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

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