Question

Suppose SAT Writing scores are normally distributed with a mean of 498 and a standard deviation of 114. A university plans to award scholarships to students whose scores are in the top 6%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

Answer 1

Answer: the minimum score required for the scholarship is 676.

Step-by-step explanation:

Suppose SAT Writing scores are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = SAT Writing scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 498

σ = 114

The probability value for the scores in the top 6% would be (1 - 6/100) = (1 - 0.06) = 0.94

Looking at the normal distribution table, the z score corresponding to the probability value is 1.56

Therefore,

1.56 = (x - 498)/114

Cross multiplying by 114, it becomes

1.56 × 114 = x - 498

177.84 = x - 498

x = 177.84 + 498

x = 676 rounded to the nearest whole number.