Question

Suppose SAT Mathematics scores are normally distributed with a mean of 518 and a standard deviation of 113. A university plans to recruit students whose scores are in the top 9%. What is the minimum score required for recruitment? Round your answer to the nearest whole number, if necessary.

Answer 1

Answer: the minimum score required for recruitment is 669

Explanation:

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

z = (x - µ)/σ

Where

x = SAT Mathematics scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 518

σ = 113

The probability value for the top 9% would be (1 - 9/100) = (1 - 0.09) = 0.91

Looking at the normal distribution table, the z score corresponding to the probability value is 1.34

Therefore,

1.34 = (x - 518)/113

Cross multiplying by 113, it becomes

1.34 × 113 = x - 518

151.42 = x - 518

x = 151.42 + 518

x = 669 to the nearest whole number.